Well-posedness of the Stokes-transport system in bounded domains and in the infinite strip
| Autor: | Antoine Leblond |
|---|---|
| Přispěvatelé: | Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Numerical Analysis, Geophysics and Ecology (ANGE), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), ANR-18-CE40-0027,SingFlows,Ecoulements avec singularités : couches limites, filaments de vortex, interaction vague-structure(2018), European Project: 637653,H2020,ERC-2014-STG,BLOC(2015), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP) |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
General Mathematics
Global well-posedness 01 natural sciences Domain (mathematical analysis) Transport equation Mathematics - Analysis of PDEs Steady Stokes equation 0103 physical sciences FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Uniqueness 0101 mathematics Mathematics Applied Mathematics 010102 general mathematics Mathematical analysis Active scalar equation Incompressible viscous uid Incompressible viscous fluid Viscous incompressible fluid Bounded function Compressibility 010307 mathematical physics Porous medium Transport system Well posedness Analysis of PDEs (math.AP) |
| Zdroj: | Journal de Mathématiques Pures et Appliquées Journal de Mathématiques Pures et Appliquées, 2022, 158, ⟨10.1016/j.matpur.2021.10.006⟩ |
| ISSN: | 0021-7824 |
| DOI: | 10.1016/j.matpur.2021.10.006⟩ |
| Popis: | We consider the Stokes-transport system, a model for the evolution of an incompressible viscous fluid with inhomogeneous density. This equation was already known to be globally well-posed for any L 1 ∩ L ∞ initial density with finite first moment in R 3 . We show that similar results hold on different domain types. We prove that the system is globally well-posed for L ∞ initial data in bounded domains of R 2 and R 3 as well as in the infinite strip R × ( 0 , 1 ) . These results contrast with the ill-posedness of a similar problem, the incompressible porous medium equation, for which uniqueness is known to fail for such a density regularity. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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