Dissipative Euler Flows with Onsager-Critical Spatial Regularity

Tristan Buckmaster; Camillo De Lellis; László Székelyhidi

doi:10.1002/cpa.21586

Dissipative Euler Flows with Onsager-Critical Spatial Regularity

Tristan Buckmaster, Camillo De Lellis, László Székelyhidi

Mathematics

Research output: Contribution to journal › Article › peer-review

69 Scopus citations

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 (Formula presented.) ; namely, x ↦ v (x,t) is ⅓−ε-Hölder continuous in space at a.e. time t and the integral (Formula presented.) is finite. A well-known open conjecture of L. Onsager claims that such solutions exist even in the class (Formula presented.).

Original language	English (US)
Pages (from-to)	1613-1670
Number of pages	58
Journal	Communications on Pure and Applied Mathematics
Volume	69
Issue number	9
DOIs	https://doi.org/10.1002/cpa.21586
State	Published - Sep 1 2016

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1002/cpa.21586

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title = "Dissipative Euler Flows with Onsager-Critical Spatial Regularity",

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 (Formula presented.) ; namely, x ↦ v (x,t) is ⅓−ε-H{\"o}lder continuous in space at a.e. time t and the integral (Formula presented.) is finite. A well-known open conjecture of L. Onsager claims that such solutions exist even in the class (Formula presented.).",

author = "Tristan Buckmaster and {De Lellis}, Camillo and L{\'a}szl{\'o} Sz{\'e}kelyhidi",

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AU - Buckmaster, Tristan

AU - De Lellis, Camillo

AU - Székelyhidi, László

PY - 2016/9/1

Y1 - 2016/9/1

N2 - 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 (Formula presented.) ; namely, x ↦ v (x,t) is ⅓−ε-Hölder continuous in space at a.e. time t and the integral (Formula presented.) is finite. A well-known open conjecture of L. Onsager claims that such solutions exist even in the class (Formula presented.).

AB - 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 (Formula presented.) ; namely, x ↦ v (x,t) is ⅓−ε-Hölder continuous in space at a.e. time t and the integral (Formula presented.) is finite. A well-known open conjecture of L. Onsager claims that such solutions exist even in the class (Formula presented.).

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JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

IS - 9

ER -

Dissipative Euler Flows with Onsager-Critical Spatial Regularity

Abstract

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