| Abstract: |
| We study the Cauchy problem for the isentropic hypo-viscous compressible Navier-Stokes equations
under general pressure laws. By using convex integration method we provides the first non-uniqueness result of weak solutions
to viscous compressible fluid. Due to the difficulties caused by the relative rigidity of the pressure and by the viscosity, our proof features new constructions of building blocks for both the
density and momentum, which are, particularly, designed to respect the compressible structure. We provide first applications of a temporally intermittent but spatially homogeneous building block scheme and a mild density perturbation. It also applies to the compressible Euler equations and the hypo-viscous incompressible Navier-Stokes equations. This is a joint work with Peng Qu, Zirong Zeng, and Deng Zhang. |
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