Statistical solutions to the Euler system of gas dynamics

TL;DR

This paper introduces a framework for constructing statistical solutions to the Euler system of gas dynamics, utilizing dissipative measure-valued solutions, entropy-based selection, and Markov semigroups to analyze compressible fluid flow.

Contribution

It presents a novel approach combining measure-valued solutions, entropy minimization, and Markov processes to study the Euler system.

Findings

Development of a dissipative measure-valued solution concept

A single-step entropy-based selection procedure

Construction of a Markov semigroup for solutions

Abstract

We consider the (complete) Euler system describing the motion of a compressible perfect fluid. We propose a platform suitable for constructing the statistical solutions. The main ingredients of our approach include: 1. The concept of dissipative (measure{valued) solution to the Euler system. 2. A single step selection procedure based on minimizing the Bregman divergence of a given solution to the maximal entropy equilibrium. 3. A construction of a Markov semigroup via push forward measures.