Global Existence for a Class of Large Solutions to the Isentropic Compressible Navier-Stokes Equations with Vacuum

In this talk, we will show the global existence and uniqueness of classical solutions with large initial energy and vacuum to the Cauchy problem for the 3D isentropic compressible Navier-Stokes equations under the assumption that the fluid is almost isothermal (i.e., $\gamma-1$ is small enough), and that the far-field density $\tilde{\rho}$ is vacuum or close to vacuum. Our results generalize the ones in [X.D. Huang, J. Li, Z.P. Xin, Comm. Pure Appl. Math. (2012)] on classical solutions with vacuum and small energy (large oscillations). This is joint work with Xiaofeng Hou, Hongyun Peng and Prof. Changjiang Zhu.