HIGAKI, Mitsuo; PRANGE, Christophe

doi:10.1007/s00526-020-01789-3

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HIGAKI, Mitsuo
Department of Mathematics, Graduate School of Science

PRANGE, Christophe
Institut de Mathématiques de Bordeaux [IMB]
Centre National de la Recherche Scientifique [CNRS]

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Ce document a été publié dans

Calculus of Variations and Partial Differential Equations. 2020, vol. 59, n° 4, p. 131

Springer Verlag

Résumé en anglais

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.< Réduire

URI

https://oskar-bordeaux.fr/handle/20.500.12278/192678

DOI

http://dx.doi.org/10.1007/s00526-020-01789-3

Project ANR

Bords, oscillations et couches limites dans les systèmes différentiels - ANR-16-CE40-0027
Ecoulements avec singularités : couches limites, filaments de vortex, interaction vague-structure - ANR-18-CE40-0027

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Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251