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arXiv · 2601.15768

Stochastically forced compressible Navier-Stokes equations with slip boundary conditions of friction type

Reo Tsuboya
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Abstract

We study a mathematical model of a compressible viscous fluid driven by stochastic forces under slip boundary conditions of friction type. We introduce a notion of a weak solution that is analytically and probabilistically consistent with this model. Our main result establishes the existence of such weak solutions under slip boundary conditions on bounded domains with $C^{2+\nu}$-boundary ($\nu>0$). The proof of this result combines an extended version of the four-layer approximation scheme on the torus by Breit/Feireisl/Hofmanov\'{a} (2018) with the convex approximation method for absolute value functions studied by Ne\v{c}asov\'{a}/Ogorzaly/Scherz (2023).

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Reo Tsuboya. 2026-01-22. Stochastically forced compressible Navier-Stokes equations with slip boundary conditions of friction type. https://arxiv.org/abs/2601.15768

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