Advances in Differential Equations

On the global well-posedness of N-dimensional generalized MHD system in anisotropic spaces

Kazuo Yamazaki

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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.


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