Solution Semiflow to the Isentropic Euler System

Dominic Breit, Eduard Feireisl, Martina Hofmanová

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)
24 Downloads (Pure)

Abstract

It is nowadays well understood that the multidimensional isentropic Euler system is desperately ill-posed. Even certain smooth initial data give rise to infinitely many solutions and all available selection criteria fail to ensure both global existence and uniqueness. We propose a different approach to the well-posedness of this system based on ideas from the theory of Markov semigroups: we show the existence of a Borel measurable solution semiflow. To this end, we introduce a notion of dissipative solution which is understood as time dependent trajectories of the basic state variables—the mass density, the linear momentum, and the energy—in a suitable phase space. The underlying system of PDEs is satisfied in a generalized sense. The solution semiflow enjoys the standard semigroup property and the solutions coincide with the strong solutions as long as the latter exist. Moreover, they minimize the energy (maximize the energy dissipation) among all dissipative solutions.
Original languageEnglish
Pages (from-to)167–194
Number of pages28
JournalArchive for Rational Mechanics and Analysis
Volume235
Early online date18 Jul 2019
DOIs
Publication statusE-pub ahead of print - 18 Jul 2019

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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