Existence and large time behaviour for a stochastic model of a modified magnetohydrodynamic equations

TL;DR

This paper analyzes a stochastic PDE system modeling turbulent non-Newtonian fluids with magnetic fields, proving the existence of solutions and their exponential decay over time.

Contribution

It introduces a mathematical framework for a coupled stochastic model of non-Newtonian fluids and magnetic fields, establishing existence and decay results.

Findings

Existence of weak martingale solutions

Exponential decay of solutions over time

Coupling of fluid dynamics and magnetic field equations

Abstract

In this paper we initiate the mathematical analysis of a system of nonlinear Stochastic Partial Differential equations describing the motion of turbulent Non-Newtonian media in the presence of fluctuating magnetic field. The system is basically obtained by a coupling of the dynamical equations of a Non-Newtonian fluids having $p$-structure and the Maxwell equations. We mainly show the existence of weak martingale solutions and their exponential decay when time goes to infinity.