Minimal Acceleration for the Multi-dimensional Isentropic Euler Equations

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 time. 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.