Publication Cover
Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 18
119
Views
5
CrossRef citations to date
0
Altmetric
Research Article

Time decay rates for the generalized MHD-α equations in Sobolev–Gevrey spaces

ORCID Icon &
Pages 6623-6644 | Received 30 Jan 2021, Accepted 29 May 2021, Published online: 11 Jun 2021

References

  • Bae H. Existence and analyticity of Lei–Lin solution to the Navier–Stokes equations. Proc Amer Math Soc. 2015;143:2887–2892.
  • Benameur J, Jlali L. Long time decay of 3D-NSE in Lei–Lin–Gevrey spaces, 2015. (arXiv:1502.04197).
  • Benameur J, Jlali L. On the blow-up criterion of 3D-NSE in Sobolev–Gevrey spaces. J Math Fluid Mech. 2016;18:805–822.
  • Catania D. Global existence for a regularized magnetohydrodynamic-α model. Ann Univ Ferrara Sez VII Sci Mat. 2010;56:1–20.
  • Chen X, Chen D. A refined regularity criterion for the strong solution to the Leray-alpha-MHD equation. Math Methods Appl Sci. 2018;41:7958–7970.
  • Guterres R, Melo WG, Nunes J, et al. Large time decay for the magnetohydrodynamics equations in Sobolev–Gevrey spaces. Monatsh Math. 2020;192:591–613. doi:10.1007/s00605-020-01415-6.
  • Jiang Z, Fan J. Time decay rate for two 3D magnetohydrodynamics-α models. Math Methods Appl Sci. 2014;37:838–845.
  • Kc D, Yamazaki K. Regularity results on the Leray-alpha magnetohydrodynamics systems. Nonlinear Anal Real World Appl. 2016;32:178–197.
  • Lorenz J, Melo WG, Rocha NF. The magneto-hydrodynamic equations: local theory and blow-up of solutions. Discrete Continuous Dyn Syst B. 2019;24:3819–3841.
  • Linshiz JS, Titi ES. Analytical study of certain magnetohydrodynamic-α models. J Math Phys. 2007;48:28.
  • Melo WG, Rocha NF, Zingano PR. Local existence, uniqueness and lower bounds of solutions for the magnetohydrodynamics equations in Sobolev–Gevrey spaces. J Math Anal Appl. 2020;482:123524.
  • Orf H. Long time decay for global solutions to the Navier–Stokes equations in Sobolev–Gevery spaces, 2019. (arXiv:1903.03034).
  • Sermange M. Some mathematical questions related to the MHD equations. Commun Pure Appl Math. 1983;36:635–664.
  • Wang Y, Li P. Global existence of three dimensional incompressible MHD flows. Math Methods Appl Sci. 2016;39:4246–4256.
  • Wang W, Qin T, Bie Q. Global well-posedness and analyticity results to 3-D generalized magnetohydrodynamic equations. Appl Math Lett. 2016;59:65–70.
  • Wu J. Generalized MHD equations. J Differ Equ. 2003;195:284–312.
  • Xiao Y, Yuan B, Zhang Q. Temporal decay estimate of solutions to 3D generalized magnetohydrodynamic system. Appl Math Lett. 2019;98:108–113.
  • Xu X, Ye Z, Note on global regularity of 3D generalized magnetohydrodynamic-α model with zero diffusivity. Commun Pure Appl Anal. 2015;14:585–595.
  • Yamazaki K. On the global regularity of generalized Leray-alpha type models. Nonlinear Anal. 2012;75:503–515.
  • Yamazaki K. Remarks on the global regularity of the two-dimensional magnetohydrodynamics system with zero dissipation. Nonlinear Anal. 2014;94:194–205.
  • Ye Z, Xu X. Global regularity of 3D generalized incompressible magnetohydrodynamic-α model. Appl Math Lett. 2014;35:1–6.
  • Ye Z. Global regularity of the two-dimensional regularized MHD equations. Dyn Partial Differ Equ. 2019;16:185–223.
  • Zhao J, Zhu M. Global regularity for the incompressible MHD-α system with fractional diffusion. Appl Math Lett. 2014;29:26–29.
  • Zhou Y, Fan J. Global Cauchy problem for a 2D Leray-α-MHD model with zero viscosity. Nonlinear Anal. 2011;74:1331–1335.
  • Holm DD. Lagrangian averages, averaged Lagrangians, and the mean effects of fluctuations in fluid dynamics. Chaos. 2002;12:518–530.
  • Melo WG, Perusato CF, Guterres RH, et al. Large time decay for the magnetohydrodynamics system in H˙s(Rn). Acta Appl Math. 2019;168:1–16. doi:10.1007/s10440-019-00276-y.
  • Zhao X, Zhu M. Decay characterization of solutions to generalized Hall-MHD system in R3. J Math Phys. 2018;59:13.
  • Bjorland C, Schonbek ME. Poincaré's inequality and diffusive evolution equations. Adv Differ Equ. 2009;14:241–260.
  • Brandolese L. Characterization of solutions to dissipative systems with sharp algebraic decay. SIAM J Math Anal. 2016;48:1616–1633.
  • Niche CJ, Schonbek ME. Decay characterization of solutions to dissipative equations. J London Math Soc. 2015;91:573–595.
  • Benameur J, Bennaceur M. Large time behaviour of solutions to the 3D-NSE in Xσ spaces. J Math Anal Appl. 2020;482:123566.
  • Lorenz J, Zingano PR. Properties at potential blow-up times for the incompressible Navier–Stokes equations. Bol Soc Paran Mat. 2017;35:127–158.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.