On the well-posedness of the Cauchy problem for an MHD system in Besov spaces

✍ Scribed by Changxing Miao; Baoquan Yuan

• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 206 KB
• Volume: 32
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1026

✦ Synopsis

Abstract

This paper is devoted to the study of the Cauchy problem of incompressible magneto‐hydrodynamics system in the framework of Besov spaces. In the case of spatial dimension n⩾3, we establish the global well‐posedness of the Cauchy problem of an incompressible magneto‐hydrodynamics system for small data and the local one for large data in the Besov space Ḃ (ℝ^n^), 1⩽p<∞ and 1⩽r⩽∞. Meanwhile, we also prove the weak–strong uniqueness of solutions with data in Ḃ (ℝ^n^)∩L^2^(ℝ^n^) for n/2__p__+2/r>1. In the case of n=2, we establish the global well‐posedness of solutions for large initial data in homogeneous Besov space Ḃ (ℝ^2^) for 2<p<∞ and 1⩽r<∞. Copyright © 2008 John Wiley & Sons, Ltd.