# Generalized solutions to models of inviscid fluids

## TL;DR

This paper introduces a new concept of dissipative solutions for the compressible Euler system, addressing oscillations and concentrations, and ensuring classical solutions under smoothness conditions.

## Contribution

It proposes a novel framework for generalized solutions of inviscid fluid models that maintains classical solution properties when smoothness is present.

## Key findings

- Dissipative solutions account for oscillations and concentrations.
- They satisfy a natural compatibility condition.
- They coincide with classical solutions when smooth.

## Abstract

We discuss several approaches to generalized solutions of problems describing the motion of inviscid fluids. We propose a new concept of dissipative solution to the compressible Euler system based on a careful analysis of possible oscillations and/or concentrations in the associated generating sequence. Unlike the conventional measure-valued solutions or rather their expected values, the dissipative solutions comply with a natural compatibility condition - they are classical solutions as long as they enjoy certain degree of smoothness.