Cauchy problem for viscous shallow water equations with a term of capillarity

2008/03/13 by Boris Haspot, Haspot, Boris
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions

paper · doi:10.48550/arxiv.0803.1939

openalex publication_date 2008/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we consider the compressible Navier-Stokes equation with density dependent viscosity coefficients and a term of capillarity introduced by Coquel et al in \cite5CR. This model includes at the same time the barotropic Navier-Stokes equations with variable viscosity coefficients, shallow-water system and the model of Rohde. We first study the well-posedness of the model in critical regularity spaces with respect to the scaling of the associated equations. In a functional setting as close as possibleto the physical energy spaces, we prove global existence of solutions close to a stable equilibrium, and local in time existence for solutions with general initial data. Uniqueness is also obtained.

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