[{"extern":"1","quality_controlled":"1","publication_status":"published","author":[{"last_name":"Killip","first_name":"Rowan","full_name":"Killip, Rowan"},{"last_name":"Masaki","full_name":"Masaki, Satoshi","first_name":"Satoshi"},{"full_name":"Murphy, Jason","first_name":"Jason","last_name":"Murphy"},{"full_name":"Visan, Monica","first_name":"Monica","last_name":"Visan","id":"056daca0-b8d1-11f0-964f-f91054abf8ca"}],"type":"journal_article","oa_version":"Preprint","citation":{"mla":"Killip, Rowan, et al. “Large Data Mass-Subcritical NLS: Critical Weighted Bounds Imply Scattering.” <i>Nonlinear Differential Equations and Applications NoDEA</i>, vol. 24, no. 4, 38, Springer Nature, 2017, doi:<a href=\"https://doi.org/10.1007/s00030-017-0463-9\">10.1007/s00030-017-0463-9</a>.","ista":"Killip R, Masaki S, Murphy J, Vişan M. 2017. Large data mass-subcritical NLS: Critical weighted bounds imply scattering. Nonlinear Differential Equations and Applications NoDEA. 24(4), 38.","short":"R. Killip, S. Masaki, J. Murphy, M. Vişan, Nonlinear Differential Equations and Applications NoDEA 24 (2017).","ama":"Killip R, Masaki S, Murphy J, Vişan M. Large data mass-subcritical NLS: Critical weighted bounds imply scattering. <i>Nonlinear Differential Equations and Applications NoDEA</i>. 2017;24(4). doi:<a href=\"https://doi.org/10.1007/s00030-017-0463-9\">10.1007/s00030-017-0463-9</a>","apa":"Killip, R., Masaki, S., Murphy, J., &#38; Vişan, M. (2017). Large data mass-subcritical NLS: Critical weighted bounds imply scattering. <i>Nonlinear Differential Equations and Applications NoDEA</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00030-017-0463-9\">https://doi.org/10.1007/s00030-017-0463-9</a>","ieee":"R. Killip, S. Masaki, J. Murphy, and M. Vişan, “Large data mass-subcritical NLS: Critical weighted bounds imply scattering,” <i>Nonlinear Differential Equations and Applications NoDEA</i>, vol. 24, no. 4. Springer Nature, 2017.","chicago":"Killip, Rowan, Satoshi Masaki, Jason Murphy, and Monica Vişan. “Large Data Mass-Subcritical NLS: Critical Weighted Bounds Imply Scattering.” <i>Nonlinear Differential Equations and Applications NoDEA</i>. Springer Nature, 2017. <a href=\"https://doi.org/10.1007/s00030-017-0463-9\">https://doi.org/10.1007/s00030-017-0463-9</a>."},"month":"06","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2026-06-22T10:26:09Z","date_created":"2026-06-19T07:32:33Z","language":[{"iso":"eng"}],"OA_place":"repository","issue":"4","status":"public","date_published":"2017-06-15T00:00:00Z","article_type":"original","scopus_import":"1","title":"Large data mass-subcritical NLS: Critical weighted bounds imply scattering","article_number":"38","intvolume":"        24","_id":"22025","publication_identifier":{"eissn":["1420-9004"],"issn":["1021-9722"]},"oa":1,"publication":"Nonlinear Differential Equations and Applications NoDEA","external_id":{"arxiv":["1606.01512"]},"arxiv":1,"publisher":"Springer Nature","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1606.01512","open_access":"1"}],"volume":24,"abstract":[{"text":"We consider the mass-subcritical nonlinear Schr¨odinger equation in all space dimensions with focusing or defocusing nonlinearity. For such equations with critical regularity sc ∈ (max{−1, −d/2 }, 0), we prove that any solution satisfying {mathematical formular} on its maximal interval of existence must be global and scatter.","lang":"eng"}],"fulldoi":"https://doi.org/10.1007/s00030-017-0463-9","OA_type":"green","day":"15","das_tickbox":"1","doi":"10.1007/s00030-017-0463-9","year":"2017"},{"status":"public","publist_id":"5960","issue":"1","language":[{"iso":"eng"}],"date_created":"2018-12-11T11:51:17Z","date_updated":"2026-09-04T11:56:53Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","article_processing_charge":"No","month":"01","citation":{"apa":"Fischer, J. L. (2014). Infinite speed of support propagation for the Derrida-Lebowitz-Speer-Spohn equation and quantum drift-diffusion models. <i>Nonlinear Differential Equations and Applications</i>. Birkhäuser. <a href=\"https://doi.org/10.1007/s00030-013-0235-0\">https://doi.org/10.1007/s00030-013-0235-0</a>","ieee":"J. L. Fischer, “Infinite speed of support propagation for the Derrida-Lebowitz-Speer-Spohn equation and quantum drift-diffusion models,” <i>Nonlinear Differential Equations and Applications</i>, vol. 21, no. 1. Birkhäuser, pp. 27–50, 2014.","ama":"Fischer JL. Infinite speed of support propagation for the Derrida-Lebowitz-Speer-Spohn equation and quantum drift-diffusion models. <i>Nonlinear Differential Equations and Applications</i>. 2014;21(1):27-50. doi:<a href=\"https://doi.org/10.1007/s00030-013-0235-0\">10.1007/s00030-013-0235-0</a>","chicago":"Fischer, Julian L. “Infinite Speed of Support Propagation for the Derrida-Lebowitz-Speer-Spohn Equation and Quantum Drift-Diffusion Models.” <i>Nonlinear Differential Equations and Applications</i>. Birkhäuser, 2014. <a href=\"https://doi.org/10.1007/s00030-013-0235-0\">https://doi.org/10.1007/s00030-013-0235-0</a>.","mla":"Fischer, Julian L. “Infinite Speed of Support Propagation for the Derrida-Lebowitz-Speer-Spohn Equation and Quantum Drift-Diffusion Models.” <i>Nonlinear Differential Equations and Applications</i>, vol. 21, no. 1, Birkhäuser, 2014, pp. 27–50, doi:<a href=\"https://doi.org/10.1007/s00030-013-0235-0\">10.1007/s00030-013-0235-0</a>.","short":"J.L. Fischer, Nonlinear Differential Equations and Applications 21 (2014) 27–50.","ista":"Fischer JL. 2014. Infinite speed of support propagation for the Derrida-Lebowitz-Speer-Spohn equation and quantum drift-diffusion models. Nonlinear Differential Equations and Applications. 21(1), 27–50."},"oa_version":"None","type":"journal_article","author":[{"orcid":"0000-0002-0479-558X","last_name":"Fischer","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","full_name":"Fischer, Julian L","first_name":"Julian L"}],"publication_status":"published","extern":"1","doi":"10.1007/s00030-013-0235-0","year":"2014","day":"01","OA_type":"closed access","fulldoi":"https://doi.org/10.1007/s00030-013-0235-0","abstract":[{"text":"We show that weak solutions of the Derrida-Lebowitz-Speer-Spohn (DLSS) equation display infinite speed of support propagation. We apply our method to the case of the quantum drift-diffusion equation which augments the DLSS equation with a drift term and possibly a second-order diffusion term. The proof is accomplished using weighted entropy estimates, Hardy's inequality and a family of singular weight functions to derive a differential inequality; the differential inequality shows exponential growth of the weighted entropy, with the growth constant blowing up very fast as the singularity of the weight becomes sharper. To the best of our knowledge, this is the first example of a nonnegativity-preserving higher-order parabolic equation displaying infinite speed of support propagation.","lang":"eng"}],"volume":21,"publisher":"Birkhäuser","publication":"Nonlinear Differential Equations and Applications","page":"27 - 50","publication_identifier":{"eissn":["1420-9004"],"issn":["1021-9722"]},"_id":"1309","intvolume":"        21","title":"Infinite speed of support propagation for the Derrida-Lebowitz-Speer-Spohn equation and quantum drift-diffusion models","article_type":"original","date_published":"2014-01-01T00:00:00Z"}]