$L^2$ decay estimates of weak solutions to 3D fractional MHD equations in exterior domains

TL;DR

This paper investigates how weak solutions to 3D fractional magnetohydrodynamic equations in exterior domains diminish over time, providing specific decay estimates under Dirichlet boundary conditions.

Contribution

It establishes $L^2$ decay estimates for weak solutions of 3D fractional MHD equations in exterior domains, advancing understanding of their long-term behavior.

Findings

Derived $L^2$ decay rates for weak solutions

Analyzed asymptotic behavior in exterior domains

Extended decay estimates to fractional MHD equations

Abstract

Consider three-dimensional fractional MHD equations in an exterior domain with the Dirichlet boundary condition assumed. Asymptotic behaviours of weak solutions to the three-dimensional exterior fractional MHD equations are studied. $L^2$ decay estimates of the weak solutions are obtained.