Critical regularity issues for the compressible Navier--Stokes system in bounded domains

2022/01/11 by Raphaël Danchin, Danchin, Raphaël, Patrick Tolksdorf +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP #math.FA

paper · pdf · doi:10.48550/arxiv.2201.03823

arxiv created 2022/01/11 · arxiv updated 2022/01/12

Abstract

We are concerned with the barotropic compressible Navier-Stokes system in a bounded domain of ℝ^d (with d≥2). In a critical regularity setting, we establish local well-posedness for large data with no vacuum and global well-posedness for small perturbations of a stable constant equilibrium state.Our results rely on new maximal regularity estimates - of independent interest - for the semigroup of the Lam\é operator, and of the linearized compressible Navier-Stokes equations.

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