The Minkowski Dimension And Hausdorff Measure Of Interior Singular Points Set Of Suitable Weak Solutions Of The Three Dimensional Of Incompressible Boussinesq Equations

In this paper, we study the partial regularity of the suitable weak solutions of the three dimensional incompressible Boussinesq equations. Using the similar method of the Ladyzhenskaya in the Navier-Stokes equations of the sufficient condition of regularity of suitable weak solutions, we get the Boussinesq equations of the sufficient condition. Using the methods of the Holder inequality, Sobolev inequality, Poincare inequality and Elliptic estimates, we obtain the related interpolation inequalities and energy inequality. By combining these conclusions, We obtain a conclusion that the Minkowski dimension of singular points set of suitable weak solution is less than 95/63 and its Hausdorff measure with respect to the gauge function h(t) = t(ln 1/t)?, (0 ?? <30/323) is 0. Moreover, the Hausdorff dimension of certain conditions of the set of singular points is less then 1.