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arXiv · 2409.13459

Local existence and conditional regularity for the Navier-Stokes-Fourier system driven by inhomogeneous boundary conditions

Anna Abbatiello·Danica Basaric·Nilasis Chaudhuri·Eduard Feireisl
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Abstract

We consider the Navier-Stokes-Fourier system with general inhomogeneous Dirichlet-Neumann boundary conditions. We propose a new approach to the local well-posedness problem based on conditional regularity estimates. By conditional regularity we mean that any strong solution belonging to a suitable class remains regular as long as its amplitude remains bounded. The result holds for general Dirichlet-Neumann boundary conditions provided the material derivative of the velocity field vanishes on the boundary of the physical domain. As a corollary of this result we obtain: Blow up criteria for strong solutions, Local existence of strong solutions in the optimal L^p-L^q framework, Alternative proof of the existing results on local well posedness.

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Anna Abbatiello, Danica Basaric, Nilasis Chaudhuri, Eduard Feireisl. 2024-09-20. Local existence and conditional regularity for the Navier-Stokes-Fourier system driven by inhomogeneous boundary conditions. https://arxiv.org/abs/2409.13459

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