DERIVING HYDRODYNAMIC EQUATIONS FOR A HAMILTONIAN “FIELD–LATTICE” SYSTEM

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

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

  1. Morrey C.B. // Commun. Pure Appl. Math. 1955. V 8. P 279-326.
  2. Olla S., Varadhan R.S.R., Yau H.-T. // Commun. Math. Phys. 1993. V. 155. P. 523-560.
  3. Esposito R., Marra R., Yau H.-T. // Commun. Math. Phys. 1996. V. 182. P. 395-456.
  4. Fritz J. An Introduction to the Theory of Hydrodynamic Limits, Lect. Math. Sci. V. 18. The Graduate School of Mathematics, Univ. Tokyo, Tokyo. 2001.
  5. Boldrighini C., Dobrushin R.L., Suhov Yu.M. // J. Stat. Phys. 1983. V. 31.N3. P. 577-615.
  6. Dobrushin R.L., Pellegrinotti A., Suhov Yu.M., Triolo L. // J. Stat. Phys. 1986. V. 43. P. 571-607.
  7. 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).
  8. 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.
  9. Spohn H. Large Scale Dynamics of Interacting Particles (Texts Monogr. Phys. V. 11). Berlin: Springer, 1991.
  10. Boldrighini C., Suhov Yu.M. // Commun. Math. Phys. 1997. V. 189. P. 577-590.
  11. Dobrushin R.L., Pellegrinotti A., Suhov Yu.M., Triolo L. // J. Stat. Phys. 1988. V. 52. P. 423-439.
  12. Дудникова Т.В. // Теорет. и матем. физика. 2011. Т. 169. N3. С. 352-367.
  13. Dudnikova T.V., Komech A.I. // Russ. J. Math. Phys. 2005. V. 12. N3. P. 301-325.
  14. Дудникова Т.В. // ДАН. 2022. Т. 506. С. 37-40.
  15. Дудникова Т.В. // Теорет. и матем. физика. 2024. Т. 218. N 2. С. 280-305.
  16. Zak J. // Phys. Rev. 1968. V. 168. P. 685-695.
  17. Dudnikova T.V. // Russ. J. Math. Phys. 2023. V. 30.N4. P. 501-521.

Supplementary files

Supplementary Files
Action
1. JATS XML

Copyright (c) 2025 Russian Academy of Sciences