Well-posedness Problem Of Two Kinds Of Fluid Equations

In this paper,we study the well-posedness results of the solutions to Magneto-Hydrodynamic equations and regularity criterion of the the Tropical climate model.First,we use the Fourier localization argument and Bony's paraproduct decomposi-tion to ensure the existence of global solutions of Generalized Magneto-hydrodynamic equations with small initial data in Fourier-Besov-Morrey spaces(F(?)_{p(·),h(·),q}^{4-2?-3/(p(·))}with variable exponents.Second,we study the regularity criterion of the Tropical cli-mate model:we obtain the classical blowup criterion for strong solutions:(1)u?L^q(0,T;L^p(R³)),u?L^q(0,T;L^p(R³)),2/q+3/p=1,3<p??,(2)?_u?L^q(0,T;L^p(R³)),2/q+3/p=2,3/2<p??;Moreover,we obtain log-blow up criterion of Tropical climate model only rely on the barotropical mode,the first baroclinic mode of vector velocity and the temperature.