Dissipative Euler flows and Onsager's conjecture

De 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 -