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