[{"date_updated":"2024-10-09T21:03:06Z","publication":"Journal of Evolution Equations","isi":1,"file_date_updated":"2022-08-16T08:52:46Z","issue":"2","scopus_import":"1","status":"public","has_accepted_license":"1","day":"01","citation":{"ama":"Agresti A, Veraar M. Nonlinear parabolic stochastic evolution equations in critical spaces part II. <i>Journal of Evolution Equations</i>. 2022;22(2). doi:<a href=\"https://doi.org/10.1007/s00028-022-00786-7\">10.1007/s00028-022-00786-7</a>","ista":"Agresti A, Veraar M. 2022. Nonlinear parabolic stochastic evolution equations in critical spaces part II. Journal of Evolution Equations. 22(2), 56.","chicago":"Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution Equations in Critical Spaces Part II.” <i>Journal of Evolution Equations</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00028-022-00786-7\">https://doi.org/10.1007/s00028-022-00786-7</a>.","mla":"Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution Equations in Critical Spaces Part II.” <i>Journal of Evolution Equations</i>, vol. 22, no. 2, 56, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s00028-022-00786-7\">10.1007/s00028-022-00786-7</a>.","ieee":"A. Agresti and M. Veraar, “Nonlinear parabolic stochastic evolution equations in critical spaces part II,” <i>Journal of Evolution Equations</i>, vol. 22, no. 2. Springer Nature, 2022.","short":"A. Agresti, M. Veraar, Journal of Evolution Equations 22 (2022).","apa":"Agresti, A., &#38; Veraar, M. (2022). Nonlinear parabolic stochastic evolution equations in critical spaces part II. <i>Journal of Evolution Equations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00028-022-00786-7\">https://doi.org/10.1007/s00028-022-00786-7</a>"},"_id":"11858","language":[{"iso":"eng"}],"abstract":[{"text":"This paper is a continuation of Part I of this project, where we developed a new local well-posedness theory for nonlinear stochastic PDEs with Gaussian noise. In the current Part II we consider blow-up criteria and regularization phenomena. As in Part I we can allow nonlinearities with polynomial growth and rough initial values from critical spaces. In the first main result we obtain several new blow-up criteria for quasi- and semilinear stochastic evolution equations. In particular, for semilinear equations we obtain a Serrin type blow-up criterium, which extends a recent result of Prüss–Simonett–Wilke (J Differ Equ 264(3):2028–2074, 2018) to the stochastic setting. Blow-up criteria can be used to prove global well-posedness for SPDEs. As in Part I, maximal regularity techniques and weights in time play a central role in the proofs. Our second contribution is a new method to bootstrap Sobolev and Hölder regularity in time and space, which does not require smoothness of the initial data. The blow-up criteria are at the basis of these new methods. Moreover, in applications the bootstrap results can be combined with our blow-up criteria, to obtain efficient ways to prove global existence. This gives new results even in classical 𝐿2-settings, which we illustrate for a concrete SPDE. In future works in preparation we apply the results of the current paper to obtain global well-posedness results and regularity for several concrete SPDEs. These include stochastic Navier–Stokes equations, reaction– diffusion equations and the Allen–Cahn equation. Our setting allows to put these SPDEs into a more flexible framework, where less restrictions on the nonlinearities are needed, and we are able to treat rough initial values from critical spaces. Moreover, we will obtain higher-order regularity results.","lang":"eng"}],"external_id":{"isi":["000809108500001"]},"type":"journal_article","quality_controlled":"1","date_published":"2022-06-01T00:00:00Z","intvolume":"        22","article_number":"56","year":"2022","ddc":["510"],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"last_name":"Agresti","full_name":"Agresti, Antonio","first_name":"Antonio","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","orcid":"0000-0002-9573-2962"},{"full_name":"Veraar, Mark","last_name":"Veraar","first_name":"Mark"}],"volume":22,"article_type":"original","month":"06","department":[{"_id":"JuFi"}],"acknowledgement":"The authors thank Emiel Lorist for helpful comments. The authors thank the anonymous referees for their helpful remarks to improve the presentation.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","oa":1,"doi":"10.1007/s00028-022-00786-7","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"corr_author":"1","article_processing_charge":"Yes (via OA deal)","publisher":"Springer Nature","file":[{"checksum":"59b99d1b48b6bd40983e7ce298524a21","file_name":"2022_Journal of Evolution Equations_Agresti.pdf","date_updated":"2022-08-16T08:52:46Z","creator":"kschuh","file_id":"11862","relation":"main_file","access_level":"open_access","success":1,"content_type":"application/pdf","date_created":"2022-08-16T08:52:46Z","file_size":1758371}],"publication_status":"published","date_created":"2022-08-16T08:39:43Z","title":"Nonlinear parabolic stochastic evolution equations in critical spaces part II","oa_version":"Published Version","publication_identifier":{"eissn":["1424-3202"],"issn":["1424-3199"]},"keyword":["Mathematics (miscellaneous)"]},{"status":"public","page":"525-537","issue":"6","ec_funded":1,"scopus_import":"1","publication":"Regular and Chaotic Dynamics","date_updated":"2025-04-14T07:53:45Z","isi":1,"intvolume":"        27","year":"2022","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_published":"2022-10-03T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2105.14640"}],"_id":"12145","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"In the class of strictly convex smooth boundaries each of which has no strip around its boundary foliated by invariant curves, we prove that the Taylor coefficients of the “normalized” Mather’s β-function are invariant under C∞-conjugacies. In contrast, we prove that any two elliptic billiard maps are C0-conjugate near their respective boundaries, and C∞-conjugate, near the boundary and away from a line passing through the center of the underlying ellipse. We also prove that, if the billiard maps corresponding to two ellipses are topologically conjugate, then the two ellipses are similar."}],"external_id":{"isi":["000865267300002"],"arxiv":["2105.14640"]},"type":"journal_article","quality_controlled":"1","day":"03","citation":{"chicago":"Koudjinan, Edmond, and Vadim Kaloshin. “On Some Invariants of Birkhoff Billiards under Conjugacy.” <i>Regular and Chaotic Dynamics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1134/S1560354722050021\">https://doi.org/10.1134/S1560354722050021</a>.","ama":"Koudjinan E, Kaloshin V. On some invariants of Birkhoff billiards under conjugacy. <i>Regular and Chaotic Dynamics</i>. 2022;27(6):525-537. doi:<a href=\"https://doi.org/10.1134/S1560354722050021\">10.1134/S1560354722050021</a>","ista":"Koudjinan E, Kaloshin V. 2022. On some invariants of Birkhoff billiards under conjugacy. Regular and Chaotic Dynamics. 27(6), 525–537.","apa":"Koudjinan, E., &#38; Kaloshin, V. (2022). On some invariants of Birkhoff billiards under conjugacy. <i>Regular and Chaotic Dynamics</i>. Springer Nature. <a href=\"https://doi.org/10.1134/S1560354722050021\">https://doi.org/10.1134/S1560354722050021</a>","mla":"Koudjinan, Edmond, and Vadim Kaloshin. “On Some Invariants of Birkhoff Billiards under Conjugacy.” <i>Regular and Chaotic Dynamics</i>, vol. 27, no. 6, Springer Nature, 2022, pp. 525–37, doi:<a href=\"https://doi.org/10.1134/S1560354722050021\">10.1134/S1560354722050021</a>.","ieee":"E. Koudjinan and V. Kaloshin, “On some invariants of Birkhoff billiards under conjugacy,” <i>Regular and Chaotic Dynamics</i>, vol. 27, no. 6. Springer Nature, pp. 525–537, 2022.","short":"E. Koudjinan, V. Kaloshin, Regular and Chaotic Dynamics 27 (2022) 525–537."},"corr_author":"1","article_processing_charge":"No","publisher":"Springer Nature","related_material":{"link":[{"url":"https://doi.org/10.1134/s1560354722060107","relation":"erratum"}]},"acknowledgement":"We are grateful to the anonymous referees for their careful reading and valuable remarks and\r\ncomments which helped to improve the paper significantly. We gratefully acknowledge support from the European Research Council (ERC) through the Advanced Grant “SPERIG” (#885707).","doi":"10.1134/S1560354722050021","oa":1,"author":[{"full_name":"Koudjinan, Edmond","last_name":"Koudjinan","orcid":"0000-0003-2640-4049","id":"52DF3E68-AEFA-11EA-95A4-124A3DDC885E","first_name":"Edmond"},{"orcid":"0000-0002-6051-2628","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","full_name":"Kaloshin, Vadim"}],"volume":27,"article_type":"original","project":[{"call_identifier":"H2020","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","grant_number":"885707","name":"Spectral rigidity and integrability for billiards and geodesic flows"}],"department":[{"_id":"VaKa"}],"month":"10","arxiv":1,"publication_identifier":{"eissn":["1468-4845"],"issn":["1560-3547"]},"keyword":["Mechanical Engineering","Applied Mathematics","Mathematical Physics","Modeling and Simulation","Statistical and Nonlinear Physics","Mathematics (miscellaneous)"],"title":"On some invariants of Birkhoff billiards under conjugacy","date_created":"2023-01-12T12:06:49Z","oa_version":"Preprint","publication_status":"published"},{"oa":1,"doi":"10.1007/s00205-021-01686-9","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). SN acknowledges partial support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – project number 405009441.","volume":242,"author":[{"orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","first_name":"Julian L","last_name":"Fischer","full_name":"Fischer, Julian L"},{"first_name":"Stefan","last_name":"Neukamm","full_name":"Neukamm, Stefan"}],"month":"06","department":[{"_id":"JuFi"}],"article_type":"original","article_processing_charge":"Yes (via OA deal)","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"publisher":"Springer Nature","publication_status":"published","file":[{"access_level":"open_access","content_type":"application/pdf","success":1,"date_created":"2021-12-16T14:58:08Z","file_size":1640121,"checksum":"cc830b739aed83ca2e32c4e0ce266a4c","file_name":"2021_ArchRatMechAnalysis_Fischer.pdf","creator":"cchlebak","date_updated":"2021-12-16T14:58:08Z","file_id":"10558","relation":"main_file"}],"keyword":["Mechanical Engineering","Mathematics (miscellaneous)","Analysis"],"publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"arxiv":1,"date_created":"2021-12-16T12:12:33Z","title":"Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems","oa_version":"Published Version","file_date_updated":"2021-12-16T14:58:08Z","date_updated":"2023-08-17T06:23:21Z","publication":"Archive for Rational Mechanics and Analysis","isi":1,"status":"public","page":"343-452","issue":"1","scopus_import":"1","external_id":{"isi":["000668431200001"],"arxiv":["1908.02273"]},"_id":"10549","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"We derive optimal-order homogenization rates for random nonlinear elliptic PDEs with monotone nonlinearity in the uniformly elliptic case. More precisely, for a random monotone operator on \\mathbb {R}^d with stationary law (that is spatially homogeneous statistics) and fast decay of correlations on scales larger than the microscale \\varepsilon >0, we establish homogenization error estimates of the order \\varepsilon in case d\\geqq 3, and of the order \\varepsilon |\\log \\varepsilon |^{1/2} in case d=2. Previous results in nonlinear stochastic homogenization have been limited to a small algebraic rate of convergence \\varepsilon ^\\delta . We also establish error estimates for the approximation of the homogenized operator by the method of representative volumes of the order (L/\\varepsilon )^{-d/2} for a representative volume of size L. Our results also hold in the case of systems for which a (small-scale) C^{1,\\alpha } regularity theory is available."}],"quality_controlled":"1","type":"journal_article","citation":{"ama":"Fischer JL, Neukamm S. Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems. <i>Archive for Rational Mechanics and Analysis</i>. 2021;242(1):343-452. doi:<a href=\"https://doi.org/10.1007/s00205-021-01686-9\">10.1007/s00205-021-01686-9</a>","ista":"Fischer JL, Neukamm S. 2021. Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems. Archive for Rational Mechanics and Analysis. 242(1), 343–452.","chicago":"Fischer, Julian L, and Stefan Neukamm. “Optimal Homogenization Rates in Stochastic Homogenization of Nonlinear Uniformly Elliptic Equations and Systems.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00205-021-01686-9\">https://doi.org/10.1007/s00205-021-01686-9</a>.","mla":"Fischer, Julian L., and Stefan Neukamm. “Optimal Homogenization Rates in Stochastic Homogenization of Nonlinear Uniformly Elliptic Equations and Systems.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 242, no. 1, Springer Nature, 2021, pp. 343–452, doi:<a href=\"https://doi.org/10.1007/s00205-021-01686-9\">10.1007/s00205-021-01686-9</a>.","short":"J.L. Fischer, S. Neukamm, Archive for Rational Mechanics and Analysis 242 (2021) 343–452.","ieee":"J. L. Fischer and S. Neukamm, “Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 242, no. 1. Springer Nature, pp. 343–452, 2021.","apa":"Fischer, J. L., &#38; Neukamm, S. (2021). Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-021-01686-9\">https://doi.org/10.1007/s00205-021-01686-9</a>"},"day":"30","has_accepted_license":"1","intvolume":"       242","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","ddc":["530"],"year":"2021","date_published":"2021-06-30T00:00:00Z"},{"article_type":"original","month":"03","volume":233,"author":[{"first_name":"Marcel","full_name":"Guardia, Marcel","last_name":"Guardia"},{"full_name":"Kaloshin, Vadim","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","first_name":"Vadim","orcid":"0000-0002-6051-2628"},{"last_name":"Zhang","full_name":"Zhang, Jianlu","first_name":"Jianlu"}],"doi":"10.1007/s00205-019-01368-7","oa":1,"extern":"1","publisher":"Springer Nature","article_processing_charge":"No","publication_status":"published","oa_version":"Published Version","date_created":"2020-09-17T10:41:51Z","title":"Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem","publication_identifier":{"issn":["0003-9527","1432-0673"]},"keyword":["Mechanical Engineering","Mathematics (miscellaneous)","Analysis"],"date_updated":"2021-01-12T08:19:09Z","publication":"Archive for Rational Mechanics and Analysis","issue":"2","status":"public","page":"799-836","citation":{"mla":"Guardia, Marcel, et al. “Asymptotic Density of Collision Orbits in the Restricted Circular Planar 3 Body Problem.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 233, no. 2, Springer Nature, 2019, pp. 799–836, doi:<a href=\"https://doi.org/10.1007/s00205-019-01368-7\">10.1007/s00205-019-01368-7</a>.","short":"M. Guardia, V. Kaloshin, J. Zhang, Archive for Rational Mechanics and Analysis 233 (2019) 799–836.","ieee":"M. Guardia, V. Kaloshin, and J. Zhang, “Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 233, no. 2. Springer Nature, pp. 799–836, 2019.","apa":"Guardia, M., Kaloshin, V., &#38; Zhang, J. (2019). Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-019-01368-7\">https://doi.org/10.1007/s00205-019-01368-7</a>","ama":"Guardia M, Kaloshin V, Zhang J. Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem. <i>Archive for Rational Mechanics and Analysis</i>. 2019;233(2):799-836. doi:<a href=\"https://doi.org/10.1007/s00205-019-01368-7\">10.1007/s00205-019-01368-7</a>","ista":"Guardia M, Kaloshin V, Zhang J. 2019. Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem. Archive for Rational Mechanics and Analysis. 233(2), 799–836.","chicago":"Guardia, Marcel, Vadim Kaloshin, and Jianlu Zhang. “Asymptotic Density of Collision Orbits in the Restricted Circular Planar 3 Body Problem.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2019. <a href=\"https://doi.org/10.1007/s00205-019-01368-7\">https://doi.org/10.1007/s00205-019-01368-7</a>."},"day":"12","type":"journal_article","quality_controlled":"1","_id":"8418","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"For the Restricted Circular Planar 3 Body Problem, we show that there exists an open set U in phase space of fixed measure, where the set of initial points which lead to collision is O(μ120) dense as μ→0."}],"main_file_link":[{"url":"https://doi.org/10.1007/s00205-019-01368-7","open_access":"1"}],"date_published":"2019-03-12T00:00:00Z","year":"2019","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"       233"},{"oa_version":"None","title":"Conservative homoclinic bifurcations and some applications","date_created":"2020-09-18T10:48:03Z","date_published":"2009-12-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","keyword":["Mathematics (miscellaneous)"],"year":"2009","publication_identifier":{"issn":["0081-5438","1531-8605"]},"intvolume":"       267","citation":{"chicago":"Gorodetski, Anton, and Vadim Kaloshin. “Conservative Homoclinic Bifurcations and Some Applications.” <i>Proceedings of the Steklov Institute of Mathematics</i>. Springer Nature, 2009. <a href=\"https://doi.org/10.1134/s0081543809040063\">https://doi.org/10.1134/s0081543809040063</a>.","ista":"Gorodetski A, Kaloshin V. 2009. Conservative homoclinic bifurcations and some applications. Proceedings of the Steklov Institute of Mathematics. 267(1), 76–90.","ama":"Gorodetski A, Kaloshin V. Conservative homoclinic bifurcations and some applications. <i>Proceedings of the Steklov Institute of Mathematics</i>. 2009;267(1):76-90. doi:<a href=\"https://doi.org/10.1134/s0081543809040063\">10.1134/s0081543809040063</a>","apa":"Gorodetski, A., &#38; Kaloshin, V. (2009). Conservative homoclinic bifurcations and some applications. <i>Proceedings of the Steklov Institute of Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1134/s0081543809040063\">https://doi.org/10.1134/s0081543809040063</a>","short":"A. Gorodetski, V. Kaloshin, Proceedings of the Steklov Institute of Mathematics 267 (2009) 76–90.","ieee":"A. Gorodetski and V. Kaloshin, “Conservative homoclinic bifurcations and some applications,” <i>Proceedings of the Steklov Institute of Mathematics</i>, vol. 267, no. 1. Springer Nature, pp. 76–90, 2009.","mla":"Gorodetski, Anton, and Vadim Kaloshin. “Conservative Homoclinic Bifurcations and Some Applications.” <i>Proceedings of the Steklov Institute of Mathematics</i>, vol. 267, no. 1, Springer Nature, 2009, pp. 76–90, doi:<a href=\"https://doi.org/10.1134/s0081543809040063\">10.1134/s0081543809040063</a>."},"day":"01","quality_controlled":"1","publication_status":"published","type":"journal_article","language":[{"iso":"eng"}],"_id":"8508","abstract":[{"lang":"eng","text":"We study generic unfoldings of homoclinic tangencies of two-dimensional area-preserving diffeomorphisms (conservative New house phenomena) and show that they give rise to invariant hyperbolic sets of arbitrarily large Hausdorff dimension. As applications, we discuss the size of the stochastic layer of a standard map and the Hausdorff dimension of invariant hyperbolic sets for certain restricted three-body problems. We avoid involved technical details and only concentrate on the ideas of the proof of the presented results."}],"extern":"1","issue":"1","status":"public","page":"76-90","publisher":"Springer Nature","article_processing_charge":"No","month":"12","article_type":"original","author":[{"last_name":"Gorodetski","full_name":"Gorodetski, Anton","first_name":"Anton"},{"last_name":"Kaloshin","full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","first_name":"Vadim"}],"volume":267,"publication":"Proceedings of the Steklov Institute of Mathematics","date_updated":"2021-01-12T08:19:46Z","doi":"10.1134/s0081543809040063"}]