Calculus of Variations and Geometric Measure Theory
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S. Daneri - L. J. Székelyhidi

Non-uniqueness and h-principle for H\"older-continuous weak solutions of the Euler equations

created by daneri on 04 Dec 2020


Published Paper

Inserted: 4 dec 2020

Journal: Arch. Rat. Mech. Anal.
Year: 2017

ArXiv: 1603.09714 PDF


In this paper we address the Cauchy problem for the incompressible Euler equations in the periodic setting. Based on estimates developed in Buckmaster-De Lellis-Isett-Székelyhidi, we prove that the set of H\"older $1\slash 5-\eps$ wild initial data is dense in $L^2$, where we call an initial datum wild if it admits infinitely many admissible H\"older $1\slash 5-\eps$ weak solutions. We also introduce a new set of stationary flows which we use as a perturbation profile instead of Beltrami flows to recover arbitrary Reynolds stresses.

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