KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
Preprint Posting Date2017-12-30
Online Publication Date2018-09-29
Print Publication Date2018-12
Permanent link to this recordhttp://hdl.handle.net/10754/626750
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AbstractIn 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.
CitationDębiec T, Gwiazda P, Świerczewska-Gwiazda A, Tzavaras A (2018) Conservation of energy for the Euler–Korteweg equations. Calculus of Variations and Partial Differential Equations 57. Available: http://dx.doi.org/10.1007/s00526-018-1441-8.
SponsorsThis 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.