A well-posedness theory in Sobolev spaces for the stochastic magnetohydrodynamic equations in the whole space

TL;DR

This paper establishes a well-posedness theory for the three-dimensional stochastic magnetohydrodynamic equations in Sobolev spaces, demonstrating the existence of solutions with initial data in these spaces.

Contribution

It provides the first well-posedness results for stochastic MHD equations in Sobolev spaces in the whole space setting.

Findings

Existence of mild solutions for stochastic MHD equations.

Solutions are constructed for initial data in Sobolev spaces.

Theoretical framework for stochastic MHD in unbounded domains.

Abstract

We prove the existence of a mild solution to the three dimensional incompressible stochastic magnetohydrodynamic equations in the whole space with the initial data which belong to the Sobolev spaces.