Global existence for the MHD system in critical spaces

Details Global existence for the MHD system in critical spaces Global existence for the MHD system in critical spaces

2008-06-20

arxiv.org/abs/0806.3417v1

Mathematics

Analysis of PDEs

31 pages, to appear in Proceedings of the Royal Society of Edinburgh. Section A. Mathematics

Scientific paper

In this article, we show that the magneto-hydrodynamic system (MHD) in $\R^N$ with variable density, variable viscosity and variable conductivity has a local weak solution in the Besov space $\dot B^{\frac{N}{p_1}}_{p_1,1}(\R^N)\times\dot B^{\frac{N}{p_2}-1}_{p_2,1}(\R^N) \times\dot B^{\frac{N}{p_2}-1}_{p_2,1}(\R^N)$ for all $1

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