Global Well-posedness Of Fractioal Navier-Stokes Equations In Variable Exponent Function Spaces

In this thesis we consider the Cauchy problem of the fractional Navier-Stokes equations in critical Fourier-Besov space with variable exponent(?).We discuss some properties of variable exponent Fourier-Besov space.The general global well-posedness of the fractional Navier-Stokes equations is obtained in variable ex-ponent Fourier-Besov space(?).In addition we also prove the global well-posedness of generalized Rotating Magneohydrodynamics equations in variable expo-nent Fourier-Besov space(?).This covers our previous result.Next,we consider the variable exponent Fourier-Besov-Morrey space(?)with s(·)=4-2?-3/(p(·)) and established the global well-posedness of fractional Navier-Stokes equations for sufficiently small initial data belonging to(?)with s(·)=4=2?-3/(p(·)).