RAS PresidiumДоклады Российской академии наук. Физика, технические науки Doklady Physics

  • ISSN (Print) 2686-7400
  • ISSN (Online) 3034-5081

DEPLETION OF NONLINEARITY FOR SPACE-ANALYTIC SPACE-PERIODIC SOLUTIONS TO EQUATIONS OF THE HYDRODYNAMIC TYPE

PII
S2686740025030023-1
DOI
10.31857/S2686740025030023
Publication type
Article
Status
Published
Authors
Volume/ Edition
Volume 522 / Issue number 1
Pages
10-15
Abstract
We consider solenoidal space-periodic space-analytic solutions to the equations of hydrodynamics. An elementary bound shows that due to the special structure of the nonlinear terms in the equations for modified solutions, effectively they lack a half of the spatial gradient. This appears to be a novel mechanism for depletion of nonlinearity. We present a two-phase iterative procedure yielding an expanded bound for the guaranteed time of the space analyticity of the hydrodynamic solutions.
Keywords
энстрофия пространственная аналитичность вырождение нелинейности
Date of publication
19.12.2024
Year of publication
2024
Number of purchasers
0
Views
19

References

  1. 1. Фриш У. Турбулентность. Наследие А. Н. Колмогорова. М.: Фазис, 1998. 343 с.
  2. 2. Matthaeus W.H., Pouquet A., Mininni P.D., Dmitruk P., Breech B. Rapid alignment of velocity and magnetic field in magnetohydrodynamic turbulence // Phys. Rev. Lett. 2008. V. 100. 085003. https://doi.org/10.1103/PhysRevLett.100.085003
  3. 3. Dorch S.B.F., Archontis V. On the saturation of astrophysical dynamos: Numerical experiments with the no-cosines flow // Solar Phys. 2004. V. 224. P. 171-178. https://doi.org/10.1007/s11207-005-5700-4
  4. 4. Donzis D.A., Gibbon J.D., Gupta A., Kerr R.M., Pandit R., Vincenzi D. Vorticity moments in four numerical simulations of the 3D Navier-Stokes equations // J. Fluid Mech. 2013. V. 732. P. 316-331. https://doi.org/10.1017/jfm.2013.409
  5. 5. Gibbon J.D., Donzis D.A., Gupta A., Kerr R.M., Pandit R., Vincenzi D. Regimes of nonlinear depletion and regularity in the 3D Navier-Stokes equations // Nonlinearity. 2014. V. 27. P. 2605-2625. https://doi.org/10.1088/0951-7715/27/10/2605
  6. 6. Gibbon J.D. Modal dependency and nonlinear depletion in the three-dimensional Navier-Stokes equations // Recent progress in the theory of the Euler and Navier-Stokes equations // Eds. Robinson J. C., Rodrigo J. L., Sadowski W., Vidal-López A. Cambridge: Cambridge University Press, 2016. P. 57-76. (London Mathematical Society Lecture Note Series. V. 430). https://doi.org/10.1017/cbo9781316407103.005
  7. 7. Gibbon J.D., Gupta A., Krstulovic G., Pandit R., Politano H., Ponty Y., Pouquet A., Sahoo G., Stawarz J. Depletion of nonlinearity in magnetohydrodynamic turbulence: Insights from analysis and simulations // Phys. Rev. E. 2016. V. 93. 043104. https://doi.org/10.1103/PhysRevE.93.043104
  8. 8. Jeyabalan S.R., Chertovskii R., Gama S., Zheligovsky V. Nonlinear large-scale perturbations of steady thermal convective dynamo regimes in a plane layer of electrically conducting fluid rotating about the vertical axis // Mathematics. 2022. V. 10. 2957. https://doi.org/10.3390/math10162957
  9. 9. Foias C., Temam R. Gevrey class regularity for the solutions of the Navier-Stokes equations // J. Funct. Anal. 1989. V. 87. P. 359-369. https://doi.org/10.1016/0022-1236 (89)90015-3
  10. 10. Bradshaw Z., Grujic Z., Kukavica I. Analyticity radii and the Navier-Stokes equations: recent results and applications // Recent progress in the theory of the Euler and Navier-Stokes equations Eds. Robinson J. C., Rodrigo J. L., Sadowski W., Vidal-López A. Cambridge University Press. 2016. P. 22-36. (London Mathematical Society Lecture Note Series. V. 430). https://doi.org/10.1017/CBO9781316407103.003
  11. 11. Zheligovsky V. Space analyticity and bounds for derivatives of solutions to the evolutionary equations of diffusive magnetohydrodynamics // Mathematics. 2021. V. 9. 1789. https://doi.org/10.3390/math9151789
  12. 12. Levermore C.D., Oliver M. Analyticity of solutions for a generalized Euler equation // J. Diff. Equations. 1997. V. 133. P. 321-339. https://doi.org/10.1006/jdeq.1996.3200
  13. 13. Zheligovsky V. A priori bounds for Gevrey-Sobolev norms of space-periodic three-dimensional solutions to equations of hydrodynamic type // Adv. Diff. Equations. 2011. V. 16. P. 955-976. https://doi.org/10.57262/ade/1355703183
  14. 14. Foias C., Guillope C., Temam R. New a priori estimates for Navier-Stokes equations in dimension 3 // Comm. Partial Diff. Equations. 1981. V. 6. P. 329-359. https://doi.org/10.1080/03605308108820180
  15. 15. Biswas A., Foias C. On the maximal space analyticity radius for the 3D Navier-Stokes equations and energy cascades // Annali di Matematica Pura ed Applicata. 2014. V. 193. P. 739-777. https://doi.org/10.1007/s10231-012-0300-z
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