On Hodge Decomposition, Effective Viscous Flux and Compressible Navier-Stokes

On Hodge Decomposition, Effective Viscous Flux and Compressible Navier-Stokes

Year:    2024

Author:    Hermano Frid, Daniel Marroquin, João Fernando Nariyoshi

Communications in Mathematical Analysis and Applications, Vol. 3 (2024), Iss. 1 : pp. 19–60

Abstract

It has been known, since the pioneering works by Serre, Hoff, Vaǐgant-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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cmaa.2024-0002

Communications in Mathematical Analysis and Applications, Vol. 3 (2024), Iss. 1 : pp. 19–60

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    42

Keywords:    Compressible Navier-Stokes equations effective viscous flux Helmholtz decomposition.

Author Details

Hermano Frid

Daniel Marroquin

João Fernando Nariyoshi