On the kinetic energy profile of Hölder continuous Euler flows
Philip Isett
Department of Mathematics, MIT, Cambridge, MA, United StatesSung-Jin Oh
Department of Mathematics, UC Berkeley, Berkeley, CA, United States
Abstract
In [8], the first author proposed a strengthening of Onsager's conjecture on the failure of energy conservation for incompressible Euler flows with Hölder regularity not exceeding . This stronger form of the conjecture implies that anomalous dissipation will fail for a generic Euler flow with regularity below the Onsager critical space due to low regularity of the energy profile.
The present paper is the second in a series of two papers whose results may be viewed as first steps towards establishing the conjectured failure of energy regularity for generic solutions with Hölder exponent less than . The main result of this paper shows that any non-negative function with compact support and Hölder regularity can be prescribed as the energy profile of an Euler flow in the class . The exponent is sharp in view of a regularity result of Isett [8]. The proof employs an improved greedy algorithm scheme that builds upon that in Buckmaster–De Lellis–Székelyhidi [1].
Cite this article
Philip Isett, Sung-Jin Oh, On the kinetic energy profile of Hölder continuous Euler flows. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 3, pp. 711–730
DOI 10.1016/J.ANIHPC.2016.05.002