Optimal Control of Stochastic Magneto-Hydrodynamics With Non-Instantaneous Impulsive Effects: Applications to Solar Flare Impact Mitigation

This article is devoted to the study of existence and optimal control for non-instantaneous impulsive incompressible stochastic magneto-hydrodynamics equation with Poisson jumps in the Hilbert space. The main objectives include establishing existence and uniqueness of mild solutions of the considered model. This is achieved in the Lp$$ {\mathtt{L}}<^>p $$ space with the help of fixed point theorem, stochastic analysis techniques and semigroup theory. Additionally, this manuscript demonstrates the existence of optimal control which is supported by Balder's theorem with an application to solar flare impact mitigation. The proposed model captures the dynamic response of the magnetized plasma to sudden and rare events in the solar wind events, providing a realistic representation of the intricate interactions between solar activity and magnetohydrodynamics in space. This work lays a foundation for advanced modeling of stochastic and impulsive systems, offering significant insights for applications in astrophysics and space weather prediction.