学术报告（郭真华 2025.4.21）

摘要：In this talk, the Cauchy problem of a compressible Navier-Stokes system with density-dependent viscosities when the initial data are spherically symmetric is considered. By dividing the Cauchy problem into two free boundary problems with the intermediately connected by a defined free boundary a(t) , we can obtain a global strong solution of the Cauchy problem after solving the existence of strong solutions of these two subissues, respectively, and piecing the solutions together. In particular, our analysis gives a positive example that it does not exhibit vacuum states provided that no vacuum states are present initially for multi-dimensional compressible flow with density-dependent viscosities, which is consistent with Hoff-Smoller where the viscosity coefficients are assumed to be positive constants.