Calculus of Variations and Geometric Measure Theory

S. Daneri - E. Runa - L. J. Székelyhidi

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

created by daneri on 04 Dec 2020


Submitted Paper

Inserted: 4 dec 2020

Year: 2020

ArXiv: 2004.00391 PDF


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 13. 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.