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arXiv · 2201.03823

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

Raphaël Danchin·Patrick Tolksdorf
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Abstract

We are concerned with the barotropic compressible Navier-Stokes system in a bounded domain of $\mathbb{R}^d$ (with $d\geq2$). 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\{\'e} operator, and of the linearized compressible Navier-Stokes equations.

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Raphaël Danchin, Patrick Tolksdorf. 2022-01-11. Critical regularity issues for the compressible Navier--Stokes system in bounded domains. https://arxiv.org/abs/2201.03823

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