[{"scopus_import":"1","issue":"3","status":"public","isi":1,"date_updated":"2023-12-13T12:08:08Z","publication":"Journal of Mathematical Fluid Mechanics","file_date_updated":"2023-08-14T07:24:17Z","date_published":"2023-08-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["510"],"year":"2023","intvolume":"        25","article_number":"72","day":"01","citation":{"ista":"Bulíček M, Málek J, Maringová E. 2023. On unsteady internal flows of incompressible fluids characterized by implicit constitutive equations in the bulk and on the boundary. Journal of Mathematical Fluid Mechanics. 25(3), 72.","ama":"Bulíček M, Málek J, Maringová E. On unsteady internal flows of incompressible fluids characterized by implicit constitutive equations in the bulk and on the boundary. <i>Journal of Mathematical Fluid Mechanics</i>. 2023;25(3). doi:<a href=\"https://doi.org/10.1007/s00021-023-00803-w\">10.1007/s00021-023-00803-w</a>","chicago":"Bulíček, Miroslav, Josef Málek, and Erika Maringová. “On Unsteady Internal Flows of Incompressible Fluids Characterized by Implicit Constitutive Equations in the Bulk and on the Boundary.” <i>Journal of Mathematical Fluid Mechanics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00021-023-00803-w\">https://doi.org/10.1007/s00021-023-00803-w</a>.","short":"M. Bulíček, J. Málek, E. Maringová, Journal of Mathematical Fluid Mechanics 25 (2023).","ieee":"M. Bulíček, J. Málek, and E. Maringová, “On unsteady internal flows of incompressible fluids characterized by implicit constitutive equations in the bulk and on the boundary,” <i>Journal of Mathematical Fluid Mechanics</i>, vol. 25, no. 3. Springer Nature, 2023.","mla":"Bulíček, Miroslav, et al. “On Unsteady Internal Flows of Incompressible Fluids Characterized by Implicit Constitutive Equations in the Bulk and on the Boundary.” <i>Journal of Mathematical Fluid Mechanics</i>, vol. 25, no. 3, 72, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00021-023-00803-w\">10.1007/s00021-023-00803-w</a>.","apa":"Bulíček, M., Málek, J., &#38; Maringová, E. (2023). On unsteady internal flows of incompressible fluids characterized by implicit constitutive equations in the bulk and on the boundary. <i>Journal of Mathematical Fluid Mechanics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00021-023-00803-w\">https://doi.org/10.1007/s00021-023-00803-w</a>"},"has_accepted_license":"1","quality_controlled":"1","type":"journal_article","external_id":{"isi":["001040354900001"],"arxiv":["2301.12834"]},"abstract":[{"lang":"eng","text":"Long-time and large-data existence of weak solutions for initial- and boundary-value problems concerning three-dimensional flows of incompressible fluids is nowadays available not only for Navier–Stokes fluids but also for various fluid models where the relation between the Cauchy stress tensor and the symmetric part of the velocity gradient is nonlinear. The majority of such studies however concerns models where such a dependence is explicit (the stress is a function of the velocity gradient), which makes the class of studied models unduly restrictive. The same concerns boundary conditions, or more precisely the slipping mechanisms on the boundary, where the no-slip is still the most preferred condition considered in the literature. Our main objective is to develop a robust mathematical theory for unsteady internal flows of implicitly constituted incompressible fluids with implicit relations between the tangential projections of the velocity and the normal traction on the boundary. The theory covers numerous rheological models used in chemistry, biorheology, polymer and food industry as well as in geomechanics. It also includes, as special cases, nonlinear slip as well as stick–slip boundary conditions. Unlike earlier studies, the conditions characterizing admissible classes of constitutive equations are expressed by means of tools of elementary calculus. In addition, a fully constructive proof (approximation scheme) is incorporated. Finally, we focus on the question of uniqueness of such weak solutions."}],"_id":"14042","language":[{"iso":"eng"}],"publisher":"Springer Nature","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)"},"department":[{"_id":"JuFi"}],"month":"08","article_type":"original","volume":25,"author":[{"full_name":"Bulíček, Miroslav","last_name":"Bulíček","first_name":"Miroslav"},{"first_name":"Josef","last_name":"Málek","full_name":"Málek, Josef"},{"full_name":"Maringová, Erika","last_name":"Maringová","first_name":"Erika","id":"dbabca31-66eb-11eb-963a-fb9c22c880b4"}],"doi":"10.1007/s00021-023-00803-w","oa":1,"acknowledgement":"M. Bulíček and J. Málek acknowledge the support of the project No. 20-11027X financed by the Czech Science foundation (GAČR). M. Bulíček and J. Málek are members of the Nečas Center for Mathematical Modelling.\r\nOpen access publishing supported by the National Technical Library in Prague.","oa_version":"Published Version","date_created":"2023-08-13T22:01:13Z","title":"On unsteady internal flows of incompressible fluids characterized by implicit constitutive equations in the bulk and on the boundary","publication_identifier":{"eissn":["1422-6952"],"issn":["1422-6928"]},"arxiv":1,"file":[{"checksum":"c549cd8f0dd02ed60477a05ca045f481","file_name":"2023_JourMathFluidMech_Bulicek.pdf","relation":"main_file","date_updated":"2023-08-14T07:24:17Z","file_id":"14046","creator":"dernst","access_level":"open_access","content_type":"application/pdf","success":1,"file_size":845748,"date_created":"2023-08-14T07:24:17Z"}],"publication_status":"published"},{"scopus_import":"1","issue":"3","ec_funded":1,"status":"public","isi":1,"date_updated":"2026-04-07T13:28:13Z","publication":"Journal of Mathematical Fluid Mechanics","file_date_updated":"2022-08-16T06:55:22Z","date_published":"2022-08-01T00:00:00Z","ddc":["510"],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","year":"2022","article_number":"93","intvolume":"        24","citation":{"mla":"Hensel, Sebastian, and Alice Marveggio. “Weak-Strong Uniqueness for the Navier–Stokes Equation for Two Fluids with Ninety Degree Contact Angle and Same Viscosities.” <i>Journal of Mathematical Fluid Mechanics</i>, vol. 24, no. 3, 93, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s00021-022-00722-2\">10.1007/s00021-022-00722-2</a>.","short":"S. Hensel, A. Marveggio, Journal of Mathematical Fluid Mechanics 24 (2022).","ieee":"S. Hensel and A. Marveggio, “Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities,” <i>Journal of Mathematical Fluid Mechanics</i>, vol. 24, no. 3. Springer Nature, 2022.","apa":"Hensel, S., &#38; Marveggio, A. (2022). Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities. <i>Journal of Mathematical Fluid Mechanics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00021-022-00722-2\">https://doi.org/10.1007/s00021-022-00722-2</a>","ama":"Hensel S, Marveggio A. Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities. <i>Journal of Mathematical Fluid Mechanics</i>. 2022;24(3). doi:<a href=\"https://doi.org/10.1007/s00021-022-00722-2\">10.1007/s00021-022-00722-2</a>","ista":"Hensel S, Marveggio A. 2022. Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities. Journal of Mathematical Fluid Mechanics. 24(3), 93.","chicago":"Hensel, Sebastian, and Alice Marveggio. “Weak-Strong Uniqueness for the Navier–Stokes Equation for Two Fluids with Ninety Degree Contact Angle and Same Viscosities.” <i>Journal of Mathematical Fluid Mechanics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00021-022-00722-2\">https://doi.org/10.1007/s00021-022-00722-2</a>."},"day":"01","has_accepted_license":"1","quality_controlled":"1","type":"journal_article","external_id":{"arxiv":["2112.11154"],"isi":["000834834300001"]},"_id":"11842","abstract":[{"text":"We consider the flow of two viscous and incompressible fluids within a bounded domain modeled by means of a two-phase Navier–Stokes system. The two fluids are assumed to be immiscible, meaning that they are separated by an interface. With respect to the motion of the interface, we consider pure transport by the fluid flow. Along the boundary of the domain, a complete slip boundary condition for the fluid velocities and a constant ninety degree contact angle condition for the interface are assumed. In the present work, we devise for the resulting evolution problem a suitable weak solution concept based on the framework of varifolds and establish as the main result a weak-strong uniqueness principle in 2D. The proof is based on a relative entropy argument and requires a non-trivial further development of ideas from the recent work of Fischer and the first author (Arch. Ration. Mech. Anal. 236, 2020) to incorporate the contact angle condition. To focus on the effects of the necessarily singular geometry of the evolving fluid domains, we work for simplicity in the regime of same viscosities for the two fluids.","lang":"eng"}],"language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"14587"}]},"publisher":"Springer Nature","article_processing_charge":"No","corr_author":"1","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)"},"month":"08","department":[{"_id":"JuFi"}],"project":[{"name":"Bridging Scales in Random Materials","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","call_identifier":"H2020","grant_number":"948819"}],"article_type":"original","volume":24,"author":[{"id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastian","orcid":"0000-0001-7252-8072","last_name":"Hensel","full_name":"Hensel, Sebastian"},{"full_name":"Marveggio, Alice","last_name":"Marveggio","first_name":"Alice","id":"25647992-AA84-11E9-9D75-8427E6697425"}],"oa":1,"doi":"10.1007/s00021-022-00722-2","acknowledgement":"The authors warmly thank their former resp. current PhD advisor Julian Fischer for the suggestion of this problem and for valuable initial discussions on the subjects of this paper. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 948819) , and from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813.","oa_version":"Published Version","date_created":"2022-08-14T22:01:45Z","title":"Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety degree contact angle and same viscosities","arxiv":1,"publication_identifier":{"issn":["1422-6928"],"eissn":["1422-6952"]},"file":[{"checksum":"75c5f286300e6f0539cf57b4dba108d5","file_name":"2022_JMathFluidMech_Hensel.pdf","file_id":"11848","creator":"cchlebak","date_updated":"2022-08-16T06:55:22Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_size":2045570,"date_created":"2022-08-16T06:55:22Z"}],"publication_status":"published"}]