no code implementations • 8 Mar 2021 • Robin Ming Chen, Alexis F. Vasseur, Cheng Yu
In dimension $n=2$ and $3$, we show that for any initial datum belonging to a dense subset of the energy space, there exist infinitely many global-in-time admissible weak solutions to the isentropic Euler system whenever $1<\gamma\leq 1+\frac2n$.
Analysis of PDEs 35Q31, 76N10, 35L65
no code implementations • 9 Oct 2020 • Geng Chen, Sam G. Krupa, Alexis F. Vasseur
As a consequence of our result, the Tame Oscillation Condition, and the Bounded Variation Condition on space-like curves are not necessary for the uniqueness of solutions in the $BV$ theory, in the case of systems with 2 unknowns.
Analysis of PDEs 35L65 (Primary) 76N15, 35L45, 35B35 (Secondary)
