Fractional Landau-Lifshitz Equation And Ginzburg-Landau Euation

In this dissertation, existence and holder regularity of weak solutions to the fractional Landau-Lifshitz equation without Gilbert damping term is proved through viscosity approximation and the inviscid limit of solution of the fractional complex Ginburg-Landau equation.For the fractional Landau-Lifshitz equation without Gilbert damping term, through viscosity approximation, we got the existence and holder regularity of weak solutions. Since the nonlinear term is nonlocal and of full order of the equation, a commutator is constructed to get the convergence of the approximating solution.For the fractional Ginzburg-Landau equationWe study the inviscid limit of the solution. It is shown that the solution of the fractional complex Ginzburg-Landau equation convergence to the solution of nonlinear fractional complex Schrodinger equation while the initial data 0u is taken in 2L, and Ha spaces as a, b tends to zero, and we also obtain the convergence rate.