Bio information: Shengguo Zhu earned his PhD in 2015 at Shanghai Jiao Tong University (joint PhD program with Georgia Tech University). He is currently a Postdoctoral Fellow at the Institute of Mathematical Sciences, Chinese University of Hong Kong.

Abstract: We present some progress on the well-posedness of classical solutions with vacuum to the Cauchy problem of the multi-dimensional compressible isentropic Navier-Stokes equations with density dependent viscosities in a power law. We will also mention some related open problems of high mathematical interest for this system. This talk is based on joint works with Yachun Li (SJTU), Ronghua Pan (Georgia Tech) and Zhouping Xin (CUHK).