Existence of global strong solution for the compressible Navier-Stokes\n equations with degenerate viscosity coefficients in 1D

2014/11/20 by Boris Haspot, Haspot, Boris · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1411.5503

openalex publication_date 2014/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider Navier-Stokes equations for compressible viscous fluids in one\ndimension. We prove the existence of global strong solution with large initial\ndata for the shallow water system. The key ingredient of the proof relies to a\nnew formulation of the compressible equations involving a new effective\nvelocity v (see citecras,para,CPAM,CPAM1) such that the density verifies a\nparabolic equation. We estimate v in L^\∞ norm which enables us to\ncontrol the vacuum on the density.\n

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