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arXiv · 2405.08390

Weak solutions to the steady incompressible Euler equations with source terms

Anxiang Huang
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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.

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Anxiang Huang. 2024-05-14. Weak solutions to the steady incompressible Euler equations with source terms. https://arxiv.org/abs/2405.08390

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