Compactly supported anomalous weak solutions for 2D Euler equations with vorticity in Hardy spaces

2024/05/29 by Buck, Miriam, Modena, Stefano · 2 citations
#35Q31 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.19214

Abstract

In a previous work (arXiv:2306.05948), we constructed by convex integration examples of energy dissipating solutions to the 2D Euler equations on ℝ² with vorticity in the real Hardy space H^p(ℝ²). In the present paper, we develop tools that significantly improve that result in two ways: Firstly, we achieve vorticities in H^p(ℝ²) in the optimal range p∈ (0,1) compared to (2/3,1) in our previous work. Secondly, the solutions constructed here possess compact support and in particular preserve linear and angular momenta.

Cited by

• Pathological solutions of Navier-Stokes equations on \mathbbT² with gradients in Hardy spaces
• Admissible solutions of the 2D Onsager's conjecture

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