报告地点：行健楼学术活动室665
邀请人：许刚教授
摘要：The global existence issue in critical spaces for compressible Navier–Stokes equations, was addressed by Danchin (Invent Math, 2000) and then developed by Charve & Danchin (ARMA, 2010); Chen, Miao & Zhang (CPAM, 2010) and Haspot (ARMA, 2011) in the Lp setting. However, whether (optimal) time-decay rates could be shown in general critical spaces and any high dimensions has remained an open question. In this talk, we introduce a pure energy argument (independent of the spectral analysis) in the general L^p critical framework, which allows not only to get the optimal time-decay rates but also to remove the smallness of low frequencies of initial data that has been crucially required in previous studies on this problem. Those time-decay results could also hold true in case of large highly oscillating initial velocities. The talk is based on a recent joint work with Z. Xin.