Global well-posedness for Deconvolution Magnetohydrodynamics models with Fractional regularization

TL;DR

This paper investigates the mathematical properties of deconvolution-based magnetohydrodynamics models with fractional regularization, establishing conditions for global well-posedness and stability in different viscous regimes.

Contribution

It provides the first rigorous analysis of existence, uniqueness, and stability for these models with optimal regularization parameters, including the special case of the Approximate Deconvolution Euler Model.

Findings

Proved global existence and uniqueness in the double viscous case.

Established optimal regularization values for well-posedness.

Demonstrated asymptotic stability under weaker regularization conditions.

Abstract

In this paper, we consider two Approximate Deconvolution Magnetohydrodynamics models which are related to Large Eddy Simulation. We first study existence and uniqueness of solutions in the double viscous case. Then, we study existence and uniqueness of solutions of the Approximate Deconvolution MHD model with magnetic diffusivity, but without kinematic viscosity. In each case, we give the optimal value of regularizations where we can prove global existence and uniqueness of the solutions. The second model includes the Approximate Deconvolution Euler Model as a particular case. Finally, an asymptotic stability result is shown in the double viscous case with weaker condition on the regularization parameter.