Well-posedness And Decay Of Solutions To Several Kinds Fractional Evolution Equations With Initial Value Problem

This paper mainly studies the global well-posedness of solutions to the initial problem of fractional Navier-Stokes-Coriolis system,and the long time behavior of solutions to the fractional incompressible Navier-Stokes equations and two dimensional dissipative quasigeostrophic equations.From the mathematical point of view,the above three kinds of fluid mechanics equation models all include the classical equation models.In fact,the study of the fractional order dissipative model is more general and more difficult than that of the classical case itself.The main theorems and proofs in Chapters 2,3 and 4.The global well-posedness of the Navier-Stokes-Coriolis equations in function space characterized by semigroups is obtained by establishing the linear and nonlinear estimates of semigroups and fixed point theorem of compression.Using Fourier analysis,H(?)lder inequality,Minkowski inequality,interpolation inequality and other tools to obtain attenuation estimation of the fractional incompressible Navier-Stokes equations and two dimensional dissipative quasigeostrophic equations.