Solvability and trajectory controllability of impulsive stochastic MHD equations with Rosenblatt process

Abstract

This manuscript is concerned with the existence and trajectory controllability of impulsive stochastic magnetohydrodynamics equation governed by the Rosenblatt process. In this work, the study is made without imposing the compactness conditions in the generator S(τ) of an analytic semigroup. The noise terms rely on both velocity and magnetic fields. Initially, we reformulated the considered system in the Hilbert space by using the Stokes operator and the existence of a mild solution is established by using Banach fixed point theorem. The trajectory controllability of the proposed model is studied in the presence of impulses using Gronwall’s inequality. An example is illustrated for the developed theoretical concepts with graphical representations.