三维不可压Boussinesq方程恰当弱解奇异点集的Minkowski维数

摘要

研究三维不可压Boussinesq方程恰当弱解的部分正则性,给出恰当弱解在某点正则的充分条件,并通过此条件及相关的能量不等式和插值不等式推出奇异点集的Minkowski维数≤95/63.%We studied the partial regularity of the suitable weak solution of the three dimensional of incompressible Boussinesq equations.We obtained the sufficient condition of regularity for suitable weak solutions,combining this result and the related interpolation inequalities and energy inequalities,we obtained a conclusion that the Minkowski dimension of singular points set of suitable weak solution was less than 95/63.