From Navier-Stokes to BV solutions of the barotropic Euler equations

Autor:	Chen, Geng, Kang, Moon-Jin, Vasseur, Alexis F.
Rok vydání:	2024
Předmět:	Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	In the realm of mathematical fluid dynamics, a formidable challenge lies in establishing inviscid limits from the Navier-Stokes equations to the Euler equations, wherein physically admissible solutions can be discerned. The pursuit of solving this intricate problem, particularly concerning singular solutions, persists in both compressible and incompressible scenarios. This article focuses on small $BV$ solutions to the barotropic Euler equation in one spatial dimension. Our investigation demonstrates that these solutions are inviscid limits for solutions to the associated compressible Navier-Stokes equation. Moreover, we extend our findings by establishing the well-posedness of such solutions within the broader class of inviscid limits of Navier-Stokes equations with locally bounded energy initial values. Comment: We fixed typos and retouched parts of the manuscript for better readability
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2401.09305 Zobrazit plný text záznamu View this record from Arxiv