Regularity for the stationary Navier-Stokes equations over bumpy boundaries and a local wall law
| Autor: | Mitsuo Higaki, Christophe Prange |
|---|---|
| Přispěvatelé: | Department of Mathematics, Graduate School of Science, Kyoto University [Kyoto], Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2019 |
| Předmět: |
Applied Mathematics
010102 general mathematics Mathematical analysis Structure (category theory) Mathematics::Analysis of PDEs Boundary (topology) Boundary layer thickness Lipschitz continuity 01 natural sciences 010101 applied mathematics Physics::Fluid Dynamics Nonlinear system Mathematics - Analysis of PDEs FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 35B27 35B65 35Q30 76D03 76D05 76D10 76M50 Boundary value problem 0101 mathematics Navier–Stokes equations Analysis Mathematics Analysis of PDEs (math.AP) |
| Zdroj: | Calculus of Variations and Partial Differential Equations Calculus of Variations and Partial Differential Equations, Springer Verlag, 2020, 59 (4), pp.131. ⟨10.1007/s00526-020-01789-3⟩ |
| ISSN: | 0944-2669 1432-0835 |
| DOI: | 10.48550/arxiv.1911.12609 |
| Popis: | We investigate regularity estimates for the stationary Navier-Stokes equations above a highly oscillating Lipschitz boundary with the no-slip boundary condition. Our main result is an improved Lipschitz regularity estimate at scales larger than the boundary layer thickness. We also obtain an improved $C^{1,\mu}$ estimate and identify the building blocks of the regularity theory, dubbed `Navier polynomials'. In the case when some structure is assumed on the oscillations of the boundary, for instance periodicity, these estimates can be seen as local error estimates. Although we handle the regularity of the nonlinear stationary Navier-Stokes equations, our results do not require any smallness assumption on the solutions. Comment: 42 pages |
| Databáze: | OpenAIRE |
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