Regularity for the stationary Navier-Stokes equations over bumpy boundaries and a local wall law
PRANGE, Christophe
Institut de Mathématiques de Bordeaux [IMB]
Centre National de la Recherche Scientifique [CNRS]
Institut de Mathématiques de Bordeaux [IMB]
Centre National de la Recherche Scientifique [CNRS]
PRANGE, Christophe
Institut de Mathématiques de Bordeaux [IMB]
Centre National de la Recherche Scientifique [CNRS]
< Reduce
Institut de Mathématiques de Bordeaux [IMB]
Centre National de la Recherche Scientifique [CNRS]
Language
en
Article de revue
This item was published in
Calculus of Variations and Partial Differential Equations. 2020, vol. 59, n° 4, p. 131
Springer Verlag
English Abstract
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 ...Read more >
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.Read less <
ANR Project
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
Ecoulements avec singularités : couches limites, filaments de vortex, interaction vague-structure - ANR-18-CE40-0027
Origin
Hal imported