No. 2020.09
Minimal acceleration for the multi-dimensional isentropic Euler equations
M. Westdickenberg
Subject: Hyperbolic conservation laws, dissipative solutions, selection
Abstract
On the set of dissipative solutions to the multi-dimensional isentropic Euler equations we introduce a quasi-order by comparing the acceleration at all times. This quasi-order is continuous with respect to a suitable notion of convergence of dissipative solutions. We establish the existence of minimal elements. Minimizing the acceleration amounts to selecting dissipative solutions that are as close to being a weak solution as possible.