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DERIVING HYDRODYNAMIC EQUATIONS FOR A HAMILTONIAN “FIELD–LATTICE” SYSTEM
- Authors: Dudnikova T.V1
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Affiliations:
- Keldysh Institute of Applied Mathematics, Russian Academy of Sciences
- Issue: Vol 521, No 1 (2025)
- Pages: 32-37
- Section: MATHEMATICS
- URL: https://journals.rcsi.science/2686-9543/article/view/289026
- DOI: https://doi.org/10.31857/S2686954325010052
- EDN: https://elibrary.ru/BTMFBR
- ID: 289026
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Abstract
We give the rigorous derivation of hydrodynamic equations for an infinite harmonic crystal coupled to the Klein–Gordon field. These equations hold in the hydrodynamic limit, and they should be considered as the analog of the Euler and Navier–Stokes equations for the model under consideration.
About the authors
T. V Dudnikova
Keldysh Institute of Applied Mathematics, Russian Academy of Sciences
Email: tdudnikov@mail.ru
Moscow, Russia
References
- Morrey C.B. // Commun. Pure Appl. Math. 1955. V 8. P 279-326.
- Olla S., Varadhan R.S.R., Yau H.-T. // Commun. Math. Phys. 1993. V. 155. P. 523-560.
- Esposito R., Marra R., Yau H.-T. // Commun. Math. Phys. 1996. V. 182. P. 395-456.
- Fritz J. An Introduction to the Theory of Hydrodynamic Limits, Lect. Math. Sci. V. 18. The Graduate School of Mathematics, Univ. Tokyo, Tokyo. 2001.
- Boldrighini C., Dobrushin R.L., Suhov Yu.M. // J. Stat. Phys. 1983. V. 31.N3. P. 577-615.
- Dobrushin R.L., Pellegrinotti A., Suhov Yu.M., Triolo L. // J. Stat. Phys. 1986. V. 43. P. 571-607.
- De Masi A., Ianiro N., Pellegrinotti A., Presutti E. // In: Nonequilibrium Phenomena II: From Stochastics to Hydrodynamics, eds. Lebowitz J.L., Montroll E.W. P. 123-294. (NorthHolland, Amsderdam, 1984).
- Добрушин Р.Л., Синай Я.Г., Сухов Ю.М. “Динамические системы статистической механики” в Динамические системы—2. Итоги науки и техн. Сер. Соврем. пробл. мат. Фундам. направления. Т. 2. М.: ВИНИТИ, 1985. С. 235-284.
- Spohn H. Large Scale Dynamics of Interacting Particles (Texts Monogr. Phys. V. 11). Berlin: Springer, 1991.
- Boldrighini C., Suhov Yu.M. // Commun. Math. Phys. 1997. V. 189. P. 577-590.
- Dobrushin R.L., Pellegrinotti A., Suhov Yu.M., Triolo L. // J. Stat. Phys. 1988. V. 52. P. 423-439.
- Дудникова Т.В. // Теорет. и матем. физика. 2011. Т. 169. N3. С. 352-367.
- Dudnikova T.V., Komech A.I. // Russ. J. Math. Phys. 2005. V. 12. N3. P. 301-325.
- Дудникова Т.В. // ДАН. 2022. Т. 506. С. 37-40.
- Дудникова Т.В. // Теорет. и матем. физика. 2024. Т. 218. N 2. С. 280-305.
- Zak J. // Phys. Rev. 1968. V. 168. P. 685-695.
- Dudnikova T.V. // Russ. J. Math. Phys. 2023. V. 30.N4. P. 501-521.
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