# Dissipative Euler flows and Onsager's conjecture

Camillo De Lellis; László Székelyhidi

Journal of the European Mathematical Society (2014)

- Volume: 016, Issue: 7, page 1467-1505
- ISSN: 1435-9855

## Access Full Article

top## Abstract

top## How to cite

topDe Lellis, Camillo, and Székelyhidi, László. "Dissipative Euler flows and Onsager's conjecture." Journal of the European Mathematical Society 016.7 (2014): 1467-1505. <http://eudml.org/doc/277168>.

@article{DeLellis2014,

abstract = {Building upon the techniques introduced in [15], for any $\theta <\frac\{1\}\{10\}$ we construct periodic weak solutions of the incompressible Euler equations which dissipate the total kinetic energy and are Hölder-continuous with exponent $\theta $. A famous conjecture of Onsager states the existence of such dissipative solutions with any Hölder exponent $\theta <\frac\{1\}\{3\}$. Our theorem is the first result in this direction.},

author = {De Lellis, Camillo, Székelyhidi, László},

journal = {Journal of the European Mathematical Society},

keywords = {Euler equations; Onsager’s conjecture; turbulence; weak periodic solutions; convex integration technique; $h$-principle; Euler equations; Onsager's conjecture; turbulence; weak periodic solutions; convex integration technique; h-principle},

language = {eng},

number = {7},

pages = {1467-1505},

publisher = {European Mathematical Society Publishing House},

title = {Dissipative Euler flows and Onsager's conjecture},

url = {http://eudml.org/doc/277168},

volume = {016},

year = {2014},

}

TY - JOUR

AU - De Lellis, Camillo

AU - Székelyhidi, László

TI - Dissipative Euler flows and Onsager's conjecture

JO - Journal of the European Mathematical Society

PY - 2014

PB - European Mathematical Society Publishing House

VL - 016

IS - 7

SP - 1467

EP - 1505

AB - Building upon the techniques introduced in [15], for any $\theta <\frac{1}{10}$ we construct periodic weak solutions of the incompressible Euler equations which dissipate the total kinetic energy and are Hölder-continuous with exponent $\theta $. A famous conjecture of Onsager states the existence of such dissipative solutions with any Hölder exponent $\theta <\frac{1}{3}$. Our theorem is the first result in this direction.

LA - eng

KW - Euler equations; Onsager’s conjecture; turbulence; weak periodic solutions; convex integration technique; $h$-principle; Euler equations; Onsager's conjecture; turbulence; weak periodic solutions; convex integration technique; h-principle

UR - http://eudml.org/doc/277168

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.