Dissipative Euler Flows with Onsager‐Critical Spatial Regularity. Issue 9 (5th June 2015)

• Record Type: Journal Article
• Authors: Buckmaster, Tristan; De Lellis, Camillo; Székelyhidi, László
• Is Part Of: Communications on pure and applied mathematics. Volume 69:Issue 9(2016:Sep.)
• Page Start: 1613
• Page End: 1670
• Publication Date: 2015-06-05
• Subjects: Mathematics -- Periodicals; Mechanics -- Periodicals; Mathématiques -- Périodiques; Mécanique -- Périodiques; 510.5
• DOI: 10.1002/cpa.21586
• Languages: English
• ISSNs: 0010-3640

Abstract

Abstract: For any ɛ > 0 we show the existence of continuous periodic weak solutions v of the Euler equations that do not conserve the kinetic energy and belong to the space L t 1 ( C x 1 / 3 − ε ) ; namely, x ↦ v ( x, t ) is ⅓−ε‐Hölder continuous in space at a.e. time t and the integral ∫ [ υ ( ⋅, t ) ] 1 / 3 − ε d t is finite. A well‐known open conjecture of L. Onsager claims that such solutions exist even in the class L t ∞ ( C x 1 / 3 − ε ) .© 2016 Wiley Periodicals, Inc.