On Non-uniqueness of continuous entropy solutions to the isentropic compressible Euler equations

Abstract

We consider the Cauchy problem for the isentropic compressible Euler equations in a three-dimensional periodic domain under general pressure laws. For any smooth initial density away from the vacuum, we construct infinitely many entropy solutions with no presence of shock. In particular, the constructed density is smooth and the momentum is $\alpha$-Hölder continuous for $\alpha <1/7$. Also, we provide a continuous entropy solution satisfying the entropy inequality strictly.

arXiv admin note: substantial text overlap with arXiv:2006.06482

References in corpus (4)

• The Riemann problem for the multidimensional isentropic system of gas dynamics is ill-posed if it contains a shock
• On Non-uniqueness of Hölder continuous globally dissipative Euler flows
• Maximum entropy production as a necessary admissibility condition for the fluid Navier-Stokes and Euler equations
• Global ill-posedness for a dense set of initial data to the Isentropic system of gas dynamics

Cited by in corpus (1)

• The Rayleigh-Taylor instability with local energy dissipation