[{"OA_type":"green","language":[{"iso":"eng"}],"publisher":"World Scientific Publishing","abstract":[{"lang":"eng","text":"Both Newtonian and non-Newtonian fluids may exhibit complex slip behaviour at the boundary. We examine a broad class of slip boundary conditions that generalises the commonly used Navier slip, perfect slip, stick-slip and Tresca friction boundary conditions. In particular, set-valued, nonmonotone, noncoercive and dynamic relations may occur. For a unifying framework of such relations, we present a fully discrete numerical scheme for the time-dependent Navier–Stokes equations subject to impermeability and general slip-type boundary conditions on polyhedral domains. Based on compactness arguments, we prove convergence of subsequences, finally ensuring the existence of a weak solution. The numerical scheme uses a general inf-sup stable pair of finite element spaces for the velocity and pressure, a regularisation approach for the implicit slip boundary condition and, most importantly, a general Nitsche method to impose the impermeability and a backward Euler time stepping. One of the key tools in the convergence proof is an inhomogeneous Korn inequality that includes a normal trace term."}],"date_created":"2026-08-16T22:01:44Z","month":"08","status":"public","publication":"Mathematical Models and Methods in Applied Sciences","mathsc":["65N30","76D07","76M10"],"oa":1,"type":"journal_article","date_published":"2026-08-04T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"epub_ahead","article_processing_charge":"No","year":"2026","doi":"10.1142/S0218202526500508","citation":{"apa":"Gazca-Orozco, P. A., Gmeineder, F., Maringová, E., &#38; Tscherpel, T. (2026). A Nitsche method for incompressible fluids with general dynamic boundary conditions. <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0218202526500508\">https://doi.org/10.1142/S0218202526500508</a>","ama":"Gazca-Orozco PA, Gmeineder F, Maringová E, Tscherpel T. A Nitsche method for incompressible fluids with general dynamic boundary conditions. <i>Mathematical Models and Methods in Applied Sciences</i>. 2026. doi:<a href=\"https://doi.org/10.1142/S0218202526500508\">10.1142/S0218202526500508</a>","ista":"Gazca-Orozco PA, Gmeineder F, Maringová E, Tscherpel T. 2026. A Nitsche method for incompressible fluids with general dynamic boundary conditions. Mathematical Models and Methods in Applied Sciences.","ieee":"P. A. Gazca-Orozco, F. Gmeineder, E. Maringová, and T. Tscherpel, “A Nitsche method for incompressible fluids with general dynamic boundary conditions,” <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing, 2026.","mla":"Gazca-Orozco, Pablo Alexei, et al. “A Nitsche Method for Incompressible Fluids with General Dynamic Boundary Conditions.” <i>Mathematical Models and Methods in Applied Sciences</i>, World Scientific Publishing, 2026, doi:<a href=\"https://doi.org/10.1142/S0218202526500508\">10.1142/S0218202526500508</a>.","short":"P.A. Gazca-Orozco, F. Gmeineder, E. Maringová, T. Tscherpel, Mathematical Models and Methods in Applied Sciences (2026).","chicago":"Gazca-Orozco, Pablo Alexei, Franz Gmeineder, Erika Maringová, and Tabea Tscherpel. “A Nitsche Method for Incompressible Fluids with General Dynamic Boundary Conditions.” <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing, 2026. <a href=\"https://doi.org/10.1142/S0218202526500508\">https://doi.org/10.1142/S0218202526500508</a>."},"department":[{"_id":"JuFi"}],"scopus_import":"1","quality_controlled":"1","oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2502.09550"}],"_id":"22718","external_id":{"arxiv":["2502.09550"]},"OA_place":"repository","arxiv":1,"day":"04","article_type":"original","publication_identifier":{"eissn":["1793-6314"],"issn":["0218-2025"]},"title":"A Nitsche method for incompressible fluids with general dynamic boundary conditions","date_updated":"2026-08-18T07:51:59Z","author":[{"last_name":"Gazca-Orozco","first_name":"Pablo Alexei","full_name":"Gazca-Orozco, Pablo Alexei"},{"full_name":"Gmeineder, Franz","last_name":"Gmeineder","first_name":"Franz"},{"full_name":"Maringová, Erika","id":"dbabca31-66eb-11eb-963a-fb9c22c880b4","last_name":"Maringová","first_name":"Erika"},{"full_name":"Tscherpel, Tabea","last_name":"Tscherpel","first_name":"Tabea"}]},{"quality_controlled":"1","oa_version":"Published Version","_id":"14042","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"doi":"10.1007/s00021-023-00803-w","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.","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>","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>","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.","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)."},"volume":25,"scopus_import":"1","department":[{"_id":"JuFi"}],"date_updated":"2026-08-18T07:47:38Z","title":"On unsteady internal flows of incompressible fluids characterized by implicit constitutive equations in the bulk and on the boundary","author":[{"full_name":"Bulíček, Miroslav","first_name":"Miroslav","last_name":"Bulíček"},{"full_name":"Málek, Josef","first_name":"Josef","last_name":"Málek"},{"full_name":"Maringová, Erika","id":"dbabca31-66eb-11eb-963a-fb9c22c880b4","last_name":"Maringová","first_name":"Erika"}],"external_id":{"isi":["001040354900001"],"arxiv":["2301.12834"]},"license":"https://creativecommons.org/licenses/by/4.0/","arxiv":1,"file_date_updated":"2023-08-14T07:24:17Z","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.","publication_identifier":{"eissn":["1422-6952"],"issn":["1422-6928"]},"article_type":"original","day":"01","month":"08","ddc":["510"],"status":"public","publication":"Journal of Mathematical Fluid Mechanics","issue":"3","intvolume":"        25","language":[{"iso":"eng"}],"publisher":"Springer Nature","has_accepted_license":"1","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"}],"date_created":"2023-08-13T22:01:13Z","article_number":"72","date_published":"2023-08-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"success":1,"file_id":"14046","date_updated":"2023-08-14T07:24:17Z","date_created":"2023-08-14T07:24:17Z","relation":"main_file","file_name":"2023_JourMathFluidMech_Bulicek.pdf","creator":"dernst","checksum":"c549cd8f0dd02ed60477a05ca045f481","file_size":845748,"access_level":"open_access","content_type":"application/pdf"}],"article_processing_charge":"Yes (via OA deal)","year":"2023","publication_status":"published","oa":1,"isi":1,"type":"journal_article"},{"scopus_import":"1","department":[{"_id":"JuFi"}],"volume":31,"project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"},{"_id":"260788DE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"W1245","name":"Dissipation and dispersion in nonlinear partial differential equations"}],"tmp":{"image":"/images/cc_by_nc_nd.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)"},"doi":"10.1142/S0218202521500470","citation":{"short":"A. Abbatiello, M. Bulíček, E. Maringová, Mathematical Models and Methods in Applied Sciences 31 (2021) 2165–2212.","chicago":"Abbatiello, Anna, Miroslav Bulíček, and Erika Maringová. “On the Dynamic Slip Boundary Condition for Navier-Stokes-like Problems.” <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing, 2021. <a href=\"https://doi.org/10.1142/S0218202521500470\">https://doi.org/10.1142/S0218202521500470</a>.","ama":"Abbatiello A, Bulíček M, Maringová E. On the dynamic slip boundary condition for Navier-Stokes-like problems. <i>Mathematical Models and Methods in Applied Sciences</i>. 2021;31(11):2165-2212. doi:<a href=\"https://doi.org/10.1142/S0218202521500470\">10.1142/S0218202521500470</a>","apa":"Abbatiello, A., Bulíček, M., &#38; Maringová, E. (2021). On the dynamic slip boundary condition for Navier-Stokes-like problems. <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0218202521500470\">https://doi.org/10.1142/S0218202521500470</a>","ista":"Abbatiello A, Bulíček M, Maringová E. 2021. On the dynamic slip boundary condition for Navier-Stokes-like problems. Mathematical Models and Methods in Applied Sciences. 31(11), 2165–2212.","ieee":"A. Abbatiello, M. Bulíček, and E. Maringová, “On the dynamic slip boundary condition for Navier-Stokes-like problems,” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 31, no. 11. World Scientific Publishing, pp. 2165–2212, 2021.","mla":"Abbatiello, Anna, et al. “On the Dynamic Slip Boundary Condition for Navier-Stokes-like Problems.” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 31, no. 11, World Scientific Publishing, 2021, pp. 2165–212, doi:<a href=\"https://doi.org/10.1142/S0218202521500470\">10.1142/S0218202521500470</a>."},"_id":"10575","oa_version":"Published Version","quality_controlled":"1","publication_identifier":{"eissn":["1793-6314"],"issn":["0218-2025"]},"article_type":"original","file_date_updated":"2022-05-16T10:55:45Z","acknowledgement":"The research of A. Abbatiello is supported by Einstein Foundation, Berlin. A. Abbatiello is also member of the Italian National Group for the Mathematical Physics (GNFM) of INdAM. M. Bulíček acknowledges the support of the project No. 20-11027X financed by Czech Science Foundation (GACR). M. Bulíček is member of the Jindřich Nečas Center for Mathematical Modelling. E. Maringová acknowledges support from Charles University Research program UNCE/SCI/023, the grant SVV-2020-260583 by the Ministry of Education, Youth and Sports, Czech Republic and from the Austrian Science Fund (FWF), grants P30000, W1245, and F65.","day":"13","arxiv":1,"license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","external_id":{"isi":["000722309400001"],"arxiv":["2009.09057"]},"author":[{"first_name":"Anna","last_name":"Abbatiello","full_name":"Abbatiello, Anna"},{"full_name":"Bulíček, Miroslav","last_name":"Bulíček","first_name":"Miroslav"},{"id":"dbabca31-66eb-11eb-963a-fb9c22c880b4","full_name":"Maringová, Erika","first_name":"Erika","last_name":"Maringová"}],"date_updated":"2025-04-15T08:31:30Z","title":"On the dynamic slip boundary condition for Navier-Stokes-like problems","has_accepted_license":"1","date_created":"2021-12-26T23:01:27Z","abstract":[{"lang":"eng","text":"The choice of the boundary conditions in mechanical problems has to reflect the interaction of the considered material with the surface. Still the assumption of the no-slip condition is preferred in order to avoid boundary terms in the analysis and slipping effects are usually overlooked. Besides the “static slip models”, there are phenomena that are not accurately described by them, e.g. at the moment when the slip changes rapidly, the wall shear stress and the slip can exhibit a sudden overshoot and subsequent relaxation. When these effects become significant, the so-called dynamic slip phenomenon occurs. We develop a mathematical analysis of Navier–Stokes-like problems with a dynamic slip boundary condition, which requires a proper generalization of the Gelfand triplet and the corresponding function space setting."}],"publisher":"World Scientific Publishing","language":[{"iso":"eng"}],"intvolume":"        31","issue":"11","publication":"Mathematical Models and Methods in Applied Sciences","ddc":["510"],"month":"10","status":"public","page":"2165-2212","isi":1,"type":"journal_article","oa":1,"article_processing_charge":"No","year":"2021","publication_status":"published","file":[{"date_updated":"2022-05-16T10:55:45Z","success":1,"file_id":"11385","access_level":"open_access","content_type":"application/pdf","file_size":795483,"file_name":"2021_MathModelsMethods_Abbatiello.pdf","checksum":"8c0a9396335f0b70e1f5cbfe450a987a","creator":"dernst","date_created":"2022-05-16T10:55:45Z","relation":"main_file"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_published":"2021-10-13T00:00:00Z"},{"issue":"09","publication":"Mathematical Models and Methods in Applied Sciences","month":"08","status":"public","publisher":"World Scientific Publishing","date_created":"2021-09-12T22:01:25Z","abstract":[{"text":"We study systems of nonlinear partial differential equations of parabolic type, in which the elliptic operator is replaced by the first-order divergence operator acting on a flux function, which is related to the spatial gradient of the unknown through an additional implicit equation. This setting, broad enough in terms of applications, significantly expands the paradigm of nonlinear parabolic problems. Formulating four conditions concerning the form of the implicit equation, we first show that these conditions describe a maximal monotone p-coercive graph. We then establish the global-in-time and large-data existence of a (weak) solution and its uniqueness. To this end, we adopt and significantly generalize Minty’s method of monotone mappings. A unified theory, containing several novel tools, is developed in a way to be tractable from the point of view of numerical approximations.","lang":"eng"}],"intvolume":"        31","language":[{"iso":"eng"}],"keyword":["Nonlinear parabolic systems","implicit constitutive theory","weak solutions","existence","uniqueness"],"article_processing_charge":"No","year":"2021","publication_status":"published","date_published":"2021-08-25T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"isi":1,"type":"journal_article","main_file_link":[{"url":"https://arxiv.org/abs/2009.06917","open_access":"1"}],"oa_version":"Preprint","quality_controlled":"1","_id":"10005","volume":31,"department":[{"_id":"JuFi"}],"scopus_import":"1","doi":"10.1142/S0218202521500457","citation":{"chicago":"Bulíček, Miroslav, Erika Maringová, and Josef Málek. “On Nonlinear Problems of Parabolic Type with Implicit Constitutive Equations Involving Flux.” <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing, 2021. <a href=\"https://doi.org/10.1142/S0218202521500457\">https://doi.org/10.1142/S0218202521500457</a>.","short":"M. Bulíček, E. Maringová, J. Málek, Mathematical Models and Methods in Applied Sciences 31 (2021).","mla":"Bulíček, Miroslav, et al. “On Nonlinear Problems of Parabolic Type with Implicit Constitutive Equations Involving Flux.” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 31, no. 09, World Scientific Publishing, 2021, doi:<a href=\"https://doi.org/10.1142/S0218202521500457\">10.1142/S0218202521500457</a>.","ieee":"M. Bulíček, E. Maringová, and J. Málek, “On nonlinear problems of parabolic type with implicit constitutive equations involving flux,” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 31, no. 09. World Scientific Publishing, 2021.","ista":"Bulíček M, Maringová E, Málek J. 2021. On nonlinear problems of parabolic type with implicit constitutive equations involving flux. Mathematical Models and Methods in Applied Sciences. 31(09).","ama":"Bulíček M, Maringová E, Málek J. On nonlinear problems of parabolic type with implicit constitutive equations involving flux. <i>Mathematical Models and Methods in Applied Sciences</i>. 2021;31(09). doi:<a href=\"https://doi.org/10.1142/S0218202521500457\">10.1142/S0218202521500457</a>","apa":"Bulíček, M., Maringová, E., &#38; Málek, J. (2021). On nonlinear problems of parabolic type with implicit constitutive equations involving flux. <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0218202521500457\">https://doi.org/10.1142/S0218202521500457</a>"},"project":[{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"author":[{"full_name":"Bulíček, Miroslav","last_name":"Bulíček","first_name":"Miroslav"},{"first_name":"Erika","last_name":"Maringová","full_name":"Maringová, Erika","id":"dbabca31-66eb-11eb-963a-fb9c22c880b4"},{"first_name":"Josef","last_name":"Málek","full_name":"Málek, Josef"}],"date_updated":"2026-08-18T07:47:39Z","title":"On nonlinear problems of parabolic type with implicit constitutive equations involving flux","arxiv":1,"article_type":"original","publication_identifier":{"eissn":["1793-6314"],"issn":["0218-2025"]},"acknowledgement":"M. Bulíček and J. Málek acknowledge the support of the project No. 18-12719S financed by the Czech\r\nScience foundation (GAČR). E. Maringová acknowledges support from Charles University Research program \r\nUNCE/SCI/023, the grant SVV-2020-260583 by the Ministry of Education, Youth and Sports, Czech Republic\r\nand from the Austrian Science Fund (FWF), grants P30000, W1245, and F65. M. Bulíček and J. Málek are\r\nmembers of the Nečas Center for Mathematical Modelling.\r\n","day":"25","external_id":{"isi":["000722222900004"],"arxiv":["2009.06917"]}}]