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

By Changxing Miao, Baoquan Yuan. 2006

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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  p,rn/p−1 (ℝn), 1⩽p<∞ and 1⩽r⩽∞. Meanwhile, we also prove the weak–strong uniqueness of solutions with data in Ḃ  p,rn/p−1 (ℝn)∩L2(ℝn) for n/2p+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  p,r2/p−1 (ℝ2) for 2

Subfields: Applied Mathematics, Mathematical Physics

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