The Well-posedness Theory And The Asymptotic Behavior Of The Fractional Navier-Stokes Equations And The Overall Well-posedness Of The Large Initial Value Solutions Of The Magnetic Fluid Equations

The thesis consists of two parts.In the first part,we study the Asymptotic behavior for the solution of the fractional Navier-Stokes system.and the other part is Global in time solutions to three-dimensional magnetohydrodynamics equations with a class of large initial data.We consider the Cauchy problem to the three-dimensional fractional Navier-Stokes system as following(?)By the Fourier localization method and the Banach fixed point,theorem,we get the existence and uniqueness of the local-in-time solution for general initial data and the global-in-time solution for small initial data in the Fourier-Herz space.Meanwhile,we obtain the decay estimates of the global solutions and show the large time behavior of the global solutions in the Fourier-Herz space.In addition,we study the Cauchy problem of the three-dimensional incompressible magnetohydrodynamics equations.(?)By introducing the weighted spaces and using the technique of microlocal analy-sis,we prove the global-in-time well-posedness of three-dimensional incompress-ible magnetohydrodynamics equations for a class of large initial data.