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arXiv · 2004.00391

Non-uniqueness for the Euler equations up to Onsager's critical exponent

Sara Daneri·Eris Runa·Laszlo Szekelyhidi Jr
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Abstract

In this paper we deal with the Cauchy problem for the incompressible Euler equations in the three-dimensional periodic setting. We prove non-uniqueness for an $L^2$-dense set of H\"older continuous initial data in the class of H\"older continuous admissible weak solutions for all exponents below the Onsager-critical $1/3$. This improves previous results on non-uniqueness obtained by Daneri in arXiv:1302.0988 and by Daneri and Szekelyhidi Jr. in arXiv:1603.09714 and generalizes the result obtained by Buckmaster, De Lellis, Szekelyhidi Jr. and Vicol in arXiv:1701.08678.

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Sara Daneri, Eris Runa, Laszlo Szekelyhidi Jr. 2020-04-01. Non-uniqueness for the Euler equations up to Onsager's critical exponent. https://arxiv.org/abs/2004.00391

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