# On convergence of approximate solutions to the compressible Euler system

@article{Feireisl2020OnCO, title={On convergence of approximate solutions to the compressible Euler system}, author={Eduard Feireisl and Martina Hofmanov'a}, journal={Annals of PDE}, year={2020} }

We consider a sequence of approximate solutions to the compressible Euler system admitting uniform energy bounds and/or satisfying the relevant field equations modulo an error vanishing in the asymptotic limit. We show that such a sequence either (i) converges strongly in the energy norm, or (ii) the limit is not a weak solution of the associated Euler system. This is in sharp contrast to the incompressible case, where (oscillatory) approximate solutions may converge weakly to solutions of the…

## 10 Citations

Approximating viscosity solutions of the Euler system

- Physics, MathematicsMath. Comput.
- 2022

It is shown how to efficiently compute a viscosity solution of the Euler system as the S-limit of numerical solutions obtained by the Viscosity Finite Volume method.

Convergence of a stochastic collocation finite volume method for the compressible Navier-Stokes system

- MathematicsArXiv
- 2021

We propose a stochastic collocation method based on the piecewise constant interpolation on the probability space combined with a finite volume method to solve the compressible Navier–Stokes system…

(S)-convergence and approximation of oscillatory solutions in fluid dynamics

- Mathematics
- 2020

We propose a new concept of (S)-convergence applicable to numerical methods as well as other consistent approximations of the Euler system in gas dynamics. (S)-convergence, based on averaging in the…

Asymptotic properties of solutions to equations of fluid dynamics

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- 2021

The goal of this lecture series is to give an overview of some recent results and new directions in continuum fluid dynamics. After a brief introduction of the basic system of balance laws, we focus…

Minimal acceleration for the multi-dimensional isentropic Euler equations

- Mathematics
- 2020

Among all dissipative solutions of the multi-dimensional isentropic Euler equations there exists at least one that minimizes the acceleration, which implies that the solution is as close to being a…

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- 2022

It is proved the existence of globalin-time measure-valued solutions for arbitrary large class of initial data and the periodic domain and using the relative energy technique, it is shown that the measure- valued solutions coincide with the classical solutions as long as the latter exist.

Limit of a Consistent Approximation to the Complete Compressible Euler System

- MathematicsJournal of Mathematical Fluid Mechanics
- 2021

The goal of the present paper is to prove that if a weak limit of a consistent approximation scheme of the compressible complete Euler system in full space $$ \mathbb {R}^d,\; d=2,3 $$
R
d…

Randomness in Compressible Fluid Flows Past an Obstacle

- MathematicsJournal of Statistical Physics
- 2022

We consider a statistical limit of solutions to the compressible Navier–Stokes system in the high Reynolds number regime in a domain exterior to a rigid body. We investigate to what extent this…

Generalized solutions to models of inviscid fluids

- MathematicsDiscrete & Continuous Dynamical Systems - B
- 2020

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…

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