PDE Seminar (2015/5/18): Global well-posedness for the compressible Navier-Stokes equations with slip boundary condition

2015-5-18 16:30 - 2015-5-18 17:30
Faculty of Science Building #3, Room 309
Miho Murata (Waseda University)
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.