The Well-posedness Of Solutions Of Fractional Anisotropic Navier-Stokes Equations

In this paper,by using Bony decomposition theory and anisotropic Littlewood-Paley frequency decomposition technique,combined with some classical tools such as Holder inequality,Bernstein inequality and interpolation inequality,obtained the trilinear operator estimation,combined with the estimation of a technical lemma and the Gronwall inequality were established the uniqueness of the weak solution of the initial value of the fractional anisotropy Navier-Stokes equation in the function space(?)(R³)when the initial value is u0?L²(R³)?(?)(R³).Secondly,it was proved that the local existence of solution u?L²([0,T];H^?)for the initial value problem of fractional-order anisotropic Navier-Stokes equations is u₀ ?H?and divu₀=0 for ?>1/3,and ?_h^?u?L2([0,T];H?).