Title Anomalous dissipation for 1/5-Hoelder Euler flows Publication Type Journal Article Year of Publication 2015 Authors Buckmaster T., De Lellis C., Isett P., L. Székelyhidi Jr. Journal Annals of Mathematics. Second Series Volume 128 Pagination 127–172 Date Published July Publisher Mathematical Sciences Publishers Type of Article euler and navier-stokes equations ISSN 0003-486X Abstract Recently the second and fourth authors developed an iterative scheme for obtaining rough solutions of the 3D incompressible Euler equations in Hölder spaces. The motivation comes from Onsager's conjecture. The construction involves a superposition of weakly interacting perturbed Beltrami flows on infinitely many scales. An obstruction to better regularity arises from the errors in the linear transport of a fast periodic flow by a slow velocity field. In a recent paper the third author has improved upon the methods and introducing some novel ideas on how to deal with this obstruction and thereby reaching a better Hölder exponent-albeit weaker than the one conjectured by Onsager. In this paper we give a shorter proof of this final result and adhering more to the original scheme of the second and fourth authors and introducing some new devices. More precisely we show that for any positive \ensuremathε, there exist periodic solutions of the 3D incompressible Euler equations that dissipate the total kinetic energy and belong to the Hölder class \$C\^ {1/5-$\backslash$epsilon}\$. Notes Ann. of Math. (2) 182 (2015), no. 1, 127–172. URL http://annals.math.princeton.edu/2015/182-1/p03 DOI 10.4007/annals.2015.182.1.3
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