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^α）for the initial value problem of fractional-order anisotropic Navier-Stokes equations is u₀ ∈Hαand divu₀=0 for α>1/3,and ∧_h^αu∈L2（[0,T];Hα）.