In [8], the first author proposed a strengthening of Onsager's conjecture on the failure of energy conservation for incompressible Euler flows with Hölder regularity not exceeding 1/3. This stronger form of the conjecture implies that anomalous dissipation will fail for a generic Euler flow with regularity below the Onsager critical space due to low regularity of the energy profile.
The present paper is the second in a series of two papers whose results may be viewed as first steps towards establishing the conjectured failure of energy regularity for generic solutions with Hölder exponent less than 1/5. The main result of this paper shows that any non-negative function with compact support and Hölder regularity 1/2 can be prescribed as the energy profile of an Euler flow in the class . The exponent 1/2 is sharp in view of a regularity result of Isett [8]. The proof employs an improved greedy algorithm scheme that builds upon that in Buckmaster–De Lellis–Székelyhidi [1].
@article{AIHPC_2017__34_3_711_0, author = {Isett, Philip and Oh, Sung-Jin}, title = {On the kinetic energy profile of {H\"older} continuous {Euler} flows}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {711--730}, publisher = {Elsevier}, volume = {34}, number = {3}, year = {2017}, doi = {10.1016/j.anihpc.2016.05.002}, zbl = {1383.35147}, mrnumber = {3633742}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2016.05.002/} }
TY - JOUR AU - Isett, Philip AU - Oh, Sung-Jin TI - On the kinetic energy profile of Hölder continuous Euler flows JO - Annales de l'I.H.P. Analyse non linéaire PY - 2017 SP - 711 EP - 730 VL - 34 IS - 3 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2016.05.002/ DO - 10.1016/j.anihpc.2016.05.002 LA - en ID - AIHPC_2017__34_3_711_0 ER -
%0 Journal Article %A Isett, Philip %A Oh, Sung-Jin %T On the kinetic energy profile of Hölder continuous Euler flows %J Annales de l'I.H.P. Analyse non linéaire %D 2017 %P 711-730 %V 34 %N 3 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2016.05.002/ %R 10.1016/j.anihpc.2016.05.002 %G en %F AIHPC_2017__34_3_711_0
Isett, Philip; Oh, Sung-Jin. On the kinetic energy profile of Hölder continuous Euler flows. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 3, pp. 711-730. doi : 10.1016/j.anihpc.2016.05.002. http://archive.numdam.org/articles/10.1016/j.anihpc.2016.05.002/
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