Non-uniqueness and h-principle for Hölder-continuous weak solutions of the Euler equations

Daneri S, Székelyhidi Jr. L (2016)

Publication Type: Other publication type

Publication year: 2016

URI: https://arxiv.org/abs/1603.09714

Abstract

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-Sz\'ekelyhidi], we prove that the set of H\"older $1\slash 5-\eps$ wild initial data is dense in L2, 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.

Authors with CRIS profile

Sara Daneri Juniorprofessur für Analysis

Involved external institutions

Universität Leipzig DE Germany (DE)

How to cite

APA:

Daneri, S., & Székelyhidi Jr., L. (2016). Non-uniqueness and h-principle for Hölder-continuous weak solutions of the Euler equations.

MLA:

Daneri, Sara, and László Székelyhidi Jr.. Non-uniqueness and h-principle for Hölder-continuous weak solutions of the Euler equations. 2016.

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