In this article we study the principle of energy conservation for the Euler–Korteweg system. We formulate an Onsager-type sufficient regularity condition for weak solutions of the Euler–Korteweg system to conserve the total energy. The result applies to the system of Quantum Hydrodynamics.
|Original language||English (US)|
|Journal||Calculus of Variations and Partial Differential Equations|
|State||Published - Sep 29 2018|
Bibliographical noteKAUST Repository Item: Exported on 2021-02-23
Acknowledgements: This work was partially supported by the Simons - Foundation Grant 346300 and the Polish Government MNiSW 2015-2019 matching fund; AET thanks the Institute of Mathematics of the Polish Academy of Sciences, Warsaw, for their hospitality during his stay as a Simons Visiting Professor, while P.G. and A.Ś-G thank KAUST for its hospitality during their stay. P.G. and A.Ś-G. received support from the National Science Centre (Poland), 2015/18/M/ST1/00075. T.D acknowledges the support of the National Science Centre (Poland), 2012/05/E/ST1/02218.