Work

Time-asymptotic self-similarity of the damped compressible Euler equations in parabolic scaling variables

Year: 2025

Type: article

Abstract: We study the long-time behavior of solutions to the compressible Euler equations with frictional damping in the whole space, where we prescribe direction-dependent values for the density at spatial infinity. To this end, we transform the system into parabolic scaling variables and derive a relative entropy inequality, which allows to conclude the convergence of the density towards a self-similar solution to the porous medium equation while the associated limit momentum is governed by Darcy's law. Moreover, we obtain convergence rates that explicitly depend on the flatness of the limit profile. While we focus on weak solutions in the one-dimensional case, we extend our results to energy-variational solutions in the multi-dimensional setting.

Source: Weierstraß-Institut für Angewandte Analysis und Stochastik

Authors: Eiter, Thomas, Schindler, Stefanie

Institution: Weierstrass Institute for Applied Analysis and Stochastics

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W6963583666

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