Special Session 2: Hyperbolic Partial Differential Equations and Applications

Non-uniqueness of weak solutions to the hypo-viscous compressible Navier-Stokes equations

Yachun LI
Shanghai Jiao Tong University
Peoples Rep of China
Co-Author(s):    
Abstract:
In this talk, I will discuss the Cauchy problem for the isentropic hypo-viscous compressible Navier-Stokes equations (CNS) under general pressure laws in all dimensions $d\geq 2$. For all hypo-viscosities $(-\Delta)^\alpha$ with $\alpha\in (0,1)$, we prove that there exist infinitely many weak solutions with certain same initial data. This talk is the joint work with Prof. Peng Qu, Prof. Deng Zhang and Dr. Zirong Zeng.