Advances in Differential Equations
- Adv. Differential Equations
- Volume 19, Number 3/4 (2014), 201-224.
On the global well-posedness of N-dimensional generalized MHD system in anisotropic spaces
Abstract
We follow the approach of [13] to study the N-dimensional generalized MHD system with fractional Laplacians as dissipative and diffusive terms in various anisotropic spaces. In particular, we obtain small initial data results with anisotropic Sobolev space type norms for which, depending on the power of the fractional Laplacians, we may decrease the regularity index in many directions to zero or even negative, in the expense of increasing the rest. Similar results in anisotropic Besov type spaces are also obtained.
Article information
Source
Adv. Differential Equations Volume 19, Number 3/4 (2014), 201-224.
Dates
First available in Project Euclid: 30 January 2014
Permanent link to this document
https://projecteuclid.org/euclid.ade/1391109084
Mathematical Reviews number (MathSciNet)
MR3161660
Zentralblatt MATH identifier
1288.35150
Subjects
Primary: 35B65: Smoothness and regularity of solutions 35Q35: PDEs in connection with fluid mechanics 35Q86: PDEs in connection with geophysics
Citation
Yamazaki, Kazuo. On the global well-posedness of N-dimensional generalized MHD system in anisotropic spaces. Adv. Differential Equations 19 (2014), no. 3/4, 201--224. https://projecteuclid.org/euclid.ade/1391109084.
