Weak solutions to the steady incompressible Euler equations with source terms

2024/05/14 by Huang, Anxiang
#76B03 35D05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.08390

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 Székelyhidi, 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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