## 偏微分方程式セミナー(2015/5/18): Global well-posedness for the compressible Navier-Stokes equations with slip boundary condition, 村田 美帆 氏

2015年 　 5月 18日 16時 30分 ～ 2015年 　 5月 18日 17時 30分

We consider a global in time unique existence theorem for the compressible viscous fluids in a bounded domain with slip boundary condition in the maximal $L_p$-$L_q$ regularity class with $2<p<\infty$ and $N<q<\infty$ under the assumption that initial data are small enough and orthogonal to rigid motions if domain is rotationally symmetric. For the purpose, we show some decay properties of solution to the linearized problem in $L_p$-$L_q$ framework. Such global well-posedness was proved by Kobayashi and Zajaczkowski in 1999 within the $L_2$ framework. One of the merits of our approach is less compatibility condition and regularity on initial data compared with the ones given by Kobayashi and Zajaczkowski. Our results are based on the joint work with Prof. Y. Shibata.