On the existence, uniqueness and regularity of strong solutions to a stochastic 2D

Abstract

A bounded domain of R 2 is used to investigate a stochastic coupled model of the Allen-Cahn equations and the stochastic magnetohydrodynamic equations. The model consists of the Allen-Cahn equation, Navier-Stokes equations and Maxwell equations (magnetic field) which are nonlinearly coupled through convection, stresses and Lorentz forces and expatiates the flow of the mixture of two incompressible, immiscible fluids under the influence of an electomagnetic field with stochastic perturbations. We demonstrate the existence, uniqueness and regularity of a strong solution. The method used is based on the Galerkin approximation, the stopping time technique and some feeble convergence principles in functional analysis.

Keywords: Stochastic, Magnetohydrodynamic, Allen-Cahn, Strong solution, Galerkin approximation.

Received Date: August 17, 2026

Accepted Date: September 09, 2026

Published Date: October 01, 2026

Available Online at: https://www.ijsrisjournal.com/index.php/ojsfiles/article/view/985