Depletion of nonlinearity for space-analytic space-periodic solutions to equations of the hydrodynamic type
- Authors: Zheligovsky V.A.1
-
Affiliations:
- Institute of Earthquake Prediction Theory and Mathematical Geophysics
- Issue: Vol 522, No 1 (2025)
- Pages: 10-15
- Section: ФИЗИКА
- URL: https://journals.rcsi.science/2686-7400/article/view/305057
- DOI: https://doi.org/10.31857/S2686740025030023
- EDN: https://elibrary.ru/pvjtij
- ID: 305057
Cite item
Abstract
About the authors
V. A. Zheligovsky
Institute of Earthquake Prediction Theory and Mathematical Geophysics
Email: vlad@mitp.ru
Moscow, Russia
References
- Фриш У. Турбулентность. Наследие А. Н. Колмогорова. М.: Фазис, 1998. 343 с.
- 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
- 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
- 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
- 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
- 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
- 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
- Jeyabalan S.R., Chertovskih 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
- 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
- Bradshaw Z., Grujić 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
- 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
- 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
- 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
- Foias C., Guillopé 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
- 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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