Conservation of energy for the Euler–Korteweg equations

Tomasz Dębiec; Piotr Gwiazda; Agnieszka Świerczewska-Gwiazda; Athanasios Tzavaras

doi:10.1007/s00526-018-1441-8

Conservation of energy for the Euler–Korteweg equations

Tomasz Dębiec, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda, Athanasios Tzavaras

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Abstract

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
Volume	57
Issue number	6
DOIs	https://doi.org/10.1007/s00526-018-1441-8
State	Published - Sep 29 2018

Bibliographical note

KAUST 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.

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Cite this

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abstract = "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.",

author = "Tomasz D{\c e}biec and Piotr Gwiazda and Agnieszka {\'S}wierczewska-Gwiazda and Athanasios Tzavaras",

note = "KAUST 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.{\'S}-G thank KAUST for its hospitality during their stay. P.G. and A.{\'S}-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.",

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AU - Dębiec, Tomasz

AU - Gwiazda, Piotr

AU - Świerczewska-Gwiazda, Agnieszka

AU - Tzavaras, Athanasios

N1 - KAUST 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.

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N2 - 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.

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Conservation of energy for the Euler–Korteweg equations

Abstract

Bibliographical note

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