{"article_processing_charge":"Yes (via OA deal)","month":"08","date_updated":"2023-12-13T12:08:08Z","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"type":"journal_article","file":[{"date_created":"2023-08-14T07:24:17Z","file_size":845748,"success":1,"file_id":"14046","date_updated":"2023-08-14T07:24:17Z","access_level":"open_access","creator":"dernst","file_name":"2023_JourMathFluidMech_Bulicek.pdf","content_type":"application/pdf","checksum":"c549cd8f0dd02ed60477a05ca045f481","relation":"main_file"}],"day":"01","department":[{"_id":"JuFi"}],"abstract":[{"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.","lang":"eng"}],"publication_status":"published","date_published":"2023-08-01T00:00:00Z","issue":"3","publisher":"Springer Nature","scopus_import":"1","oa_version":"Published Version","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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","quality_controlled":"1","status":"public","external_id":{"isi":["001040354900001"],"arxiv":["2301.12834"]},"publication_identifier":{"issn":["1422-6928"],"eissn":["1422-6952"]},"author":[{"first_name":"Miroslav","last_name":"Bulíček","full_name":"Bulíček, Miroslav"},{"first_name":"Josef","last_name":"Málek","full_name":"Málek, Josef"},{"id":"dbabca31-66eb-11eb-963a-fb9c22c880b4","full_name":"Maringová, Erika","first_name":"Erika","last_name":"Maringová"}],"publication":"Journal of Mathematical Fluid Mechanics","has_accepted_license":"1","doi":"10.1007/s00021-023-00803-w","_id":"14042","article_number":"72","language":[{"iso":"eng"}],"citation":{"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>.","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.","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>","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>","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>.","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.","short":"M. Bulíček, J. Málek, E. Maringová, Journal of Mathematical Fluid Mechanics 25 (2023)."},"article_type":"original","year":"2023","intvolume":"        25","volume":25,"ddc":["510"],"file_date_updated":"2023-08-14T07:24:17Z","isi":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."}