Some results on the well-posedness of Euler-Voigt and Navier-Stokes-Voigt models

TL;DR

This paper investigates the stability of Euler-Voigt and Navier-Stokes-Voigt models, demonstrating their structural stability with respect to changes in regularization parameters, contributing to understanding their well-posedness.

Contribution

It establishes the structural stability of Euler-Voigt and Navier-Stokes-Voigt models under variations of regularization parameters, advancing the theoretical understanding of their well-posedness.

Findings

Models are structurally stable under parameter variations

Results support the robustness of regularized fluid models

Provides insights into the well-posedness of these models

Abstract

We consider the Euler-Voigt equations and the Navier-Stokes-Voigt equations, which are obtained by an inviscid alpha-regularization from the corresponding equations. The main result we show is the structural stability of the system in term of the variations of both viscosity of regularization parameters.