Research On The Stability Of The Solution Of MHD Equations

This paper mainly studies the stability of the solution of the two-dimensional incompressible MHD equation with velocity damping terms.Because the global well-posedness of the large initial smooth solution of the three-dimensional incompressible Navier-stokes equation is still one of the unsolved problems in the mathematical world.The researched MHD equation has many similarities with it in structure,so it has positive research value.In the second chapter,we added the velocity damping term to the original MHD equation and gave a laminar solution that satisfies the equation.Using the method of separating variables,the good properties and boundary conditions of the laminar solution are found,and small disturbances are applied on the basis of it.Through the energy construction and weighted estimation,the problem of derivative loss is overcome.As time goes on,the layer is finally proved Exponential stability of flow solution.