The Global Existence Of The Blow-up Lower Bound And Euler Equations For The Navier-Stokes Equations

In this paper,we study the existence of the global solution of the Euler equation and the lower bound of the solution of the Navier-Stokes equation,by using the interpolation inequality,we get the lower bound of the solution of the Navier-Stokes equation in the homogeneous Sobolev spaceH~s(s≥3/2)and generalize the results of Younsi[26]work;for the three dimensional Navier-Stokes equation with the Coriolis force,the results of the general Navier-Stokes equations are generalized to the Navier-Stokes equation with the Coriolis force,by using Littlewood-Paley decomposition,we get the lower bound of the solution in the homogeneous Sobolev space H~s(s≥3/2);we also study the global existence and uniqueness of solutions of Euler equations,by studying the local existence and bursting results of Euler equation in weakly Besov spaces and using the operator estimation and embedding property to estimate the norm of the solution and the pressure term,it is proved that the global existence and uniqueness of the solution of the Euler equation in the weak Besov space (?),1<p<∞,s>n/p+1,1≤r≤∞ when it is n= 2.