On Hodge decomposition, effective viscous flux and compressible Navier-Stokes

2020/10/09 by Hermano Frid, Frid, Hermano, Daniel Marroquin +3
Engineering · Mathematics · #35Q35 #76N06 #76N10 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2010.04850

openalex publication_date 2020/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It has been known, since the pioneering works by Serre, Hoff, Vaĭgant-Kazhikhov, Lions and Feireisl, among others, the regularizing properties of the effective viscous flux and its characterization as the function whose gradient is the gradient part in the Hodge decomposition of the Newtonian force of the fluid, when the shear viscosity of the fluid is constant. In this article, we explore further the connection between the Hodge decomposition of the Newtonian force and the regularizing properties of its gradient part, by addressing the problem of the global existence of weak solutions for compressible Navier-Stokes equations with both viscosities depending on a spatial mollification of the density.

Citations

• On commutators of singular integrals and bilinear singular integrals
• Global Existence of Weak Solutions to the Barotropic Compressible Navier-Stokes Flows with Degenerate Viscosities

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