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

Abstract

This paper proves the existence of a unique global in time solution for the generalized Magnetohydrodynamics-α equations in Sobolev–Gevrey (and Sobolev) spaces (including critical cases) if it is assumed that the initial data is small enough. In addition, the authors show that this same solution is analytic and study its long time behavior.

Keywords:

• Generalized MHD-α equations
• global asymptotic solution
• decay rates
• Sobolev–Gevrey spaces

AMS Mathematics Subject Classifications:

• 35Q30
• 76D05
• 76W05
• 35A05
• 35B40

Acknowledgments

The author Thyago S. R. Santos is partially supported by CNPq grant 134250/2019-2.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This author was partially supported by CNPq grant 134250/2019-2