Weak solutions to the steady incompressible Euler equations with source terms
Analysis of PDEs
2024-05-15 v1
Abstract
In this paper, we prove the non-uniqueness of stationary solutions to steady incompressible Euler equations with source terms. Based on the convex integration scheme developed by De Lellis and Sz\'{e}kelyhidi, the Euler system is reformulated as a differential inclusion. The key point is to construct the corresponding plane-wave solutions via high frequency perturbations. Then we use iteration and Baire category argument to conclude that there exist a large amount of weak solutions with given energy profile.
Cite
@article{arxiv.2405.08390,
title = {Weak solutions to the steady incompressible Euler equations with source terms},
author = {Anxiang Huang},
journal= {arXiv preprint arXiv:2405.08390},
year = {2024}
}