Minimal acceleration for the multi-dimensional isentropic Euler equations

arXiv (Cornell University)

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.

Authors 1

1. Michael Westdickenberg corresponding Aachen Lehrstuhl für Mathematik (Analysis)

   RWTH Aachen University

   Affiliation as printed

   Lehrstuhl für Mathematik (Analysis) , RWTH Aachen Uni- versity , Templergraben 55 , D-52062 Aachen , Germany