# Ill-posedness for bounded admissible solutions of the $2$-dimensional $p$-system

created by delellis on 02 Jul 2013

[BibTeX]

Published Paper

Inserted: 2 jul 2013
Last Updated: 2 jul 2013

Journal: Hyperbolic problems: theory, numerics and applications.
Volume: 67 of Proc. Sympos. Appl. Math.
Pages: 269-278
Year: 2009

Abstract:

Consider the $p$--system of isentropic gas dynamics in $n$ space dimensions, where $n\geq 2$. In a recent joint work with L\'aszl\'o Sz\'ekelyhidi we showed bounded initial data for which this system has infinitely many admissible solutions. Moreover, the solutions and the initial data are bounded away from the void. Our result builds on an earlier work, where we introduced a new tool to generate wild solutions to the Euler equations for incompressible fluids.