Geodesic
Anomalous dissipation for $1/5$-Hölder Euler flows
Tristan Buckmaster1 ; Camillo De Lellis2 ; Philip Isett3 ; László Székelyhidi, Jr.4
1 Institut für Mathematik, Universität Leipzig, Leipzig, Germany
2 Institut für Mathematik, Universität Zürich, Zürich, Winterthurerstrasse 190, CH-190 ü, Switzerland
3 Department of Mathematics, Princeton University, Princeton, NJ
4 Institut für Mathematik, Universität Leipzig, Augustusplatz 10, 04109 Leipzig, Germany
Annals of mathematics, Tome 182 (2015) no. 1, pp. 127-172.

Voir la notice de l'article provenant de la source Annals of Mathematics website

Recently the second and fourth authors developed an iterative scheme for obtaining rough solutions of the 3D incompressible Euler equations in Hölder spaces. The motivation comes from Onsager’s conjecture. The construction involves a superposition of weakly interacting perturbed Beltrami flows on infinitely many scales. An obstruction to better regularity arises from the errors in the linear transport of a fast periodic flow by a slow velocity field.
In a recent paper the third author has improved upon the methods, introducing some novel ideas on how to deal with this obstruction, thereby reaching a better Hölder exponent — albeit weaker than the one conjectured by Onsager. In this paper we give a shorter proof of this final result, adhering more to the original scheme of the second and fourth authors and introducing some new devices. More precisely we show that for any positive $\varepsilon$, there exist periodic solutions of the 3D incompressible Euler equations that dissipate the total kinetic energy and belong to the Hölder class $C^{1/5-\varepsilon}$.
DOI : 10.4007/annals.2015.182.1.3

Tristan Buckmaster 1 ; Camillo De Lellis 2 ; Philip Isett 3 ; László Székelyhidi, Jr. 4

1 Institut für Mathematik, Universität Leipzig, Leipzig, Germany
2 Institut für Mathematik, Universität Zürich, Zürich, Winterthurerstrasse 190, CH-190 ü, Switzerland
3 Department of Mathematics, Princeton University, Princeton, NJ
4 Institut für Mathematik, Universität Leipzig, Augustusplatz 10, 04109 Leipzig, Germany 
@article{10_4007_annals_2015_182_1_3,
     author = {Tristan Buckmaster and Camillo De Lellis and Philip Isett and L\'aszl\'o Sz\'ekelyhidi, Jr.},
     title = {Anomalous dissipation for $1/5${-H\"older} {Euler} flows},
     journal = {Annals of mathematics},
     pages = {127--172},
     publisher = {mathdoc},
     volume = {182},
     number = {1},
     year = {2015},
     doi = {10.4007/annals.2015.182.1.3},
     mrnumber = {3374958},
     zbl = {06456007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2015.182.1.3/}
}
TY  - JOUR
AU  - Tristan Buckmaster
AU  - Camillo De Lellis
AU  - Philip Isett
AU  - László Székelyhidi, Jr.
TI  - Anomalous dissipation for $1/5$-Hölder Euler flows
JO  - Annals of mathematics
PY  - 2015
SP  - 127
EP  - 172
VL  - 182
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2015.182.1.3/
DO  - 10.4007/annals.2015.182.1.3
LA  - en
ID  - 10_4007_annals_2015_182_1_3
ER  - 
%0 Journal Article
%A Tristan Buckmaster
%A Camillo De Lellis
%A Philip Isett
%A László Székelyhidi, Jr.
%T Anomalous dissipation for $1/5$-Hölder Euler flows
%J Annals of mathematics
%D 2015
%P 127-172
%V 182
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2015.182.1.3/
%R 10.4007/annals.2015.182.1.3
%G en
%F 10_4007_annals_2015_182_1_3
Tristan Buckmaster; Camillo De Lellis; Philip Isett; László Székelyhidi, Jr. Anomalous dissipation for $1/5$-Hölder Euler flows. Annals of mathematics, Tome 182 (2015) no. 1, pp. 127-172. doi : 10.4007/annals.2015.182.1.3. http://geodesic.mathdoc.fr/articles/10.4007/annals.2015.182.1.3/

Cité par Sources :