半空间上Boussinesq方程组弱解的L^2衰减估计

The L^2 decay of the weak solution of the Boussinesq equations in half space

主要研究外力函数f满足一定条件时,半空间上Boussinesq方程组当n≥3时弱解的L2衰减.先假设解光滑,给出了光滑解的一致L2衰减估计,再通过构造逼近解,对逼近解序列作一致衰减估计,取极限得到弱解的一致L2衰减估计.

This paper is mainly concerned with the L2 decay the weak solution of the Boussinesq equations in half space under the appropriate assumption of the external force f . Frist the paper gives uniform L2 decay estimate of smooth solution under the assumption that the solution is smooth. Then the paper construcs approximate solution and gives uniform decay estimate of the approximate solution. Finally, the theorem is proved by taking limit.