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Global Classical Solutions to the Equations of Two–dimensional MHD Transverse Flow

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Abstract

A new method for constructing the symmetric form for the hyperbolic systems is introduced. Then a new symmetric form of the equations of MHD transverse flow is constructed by adding an additional equation. With this new form, we obtain the local existence of smooth solution including the case that the initial density may tend to the vacuum state at infinity. Furthermore, the uniformly a priori estimation for the classical solutions is established and the global smooth solutions for a kind of initial data are obtained.

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  1. State Key Laboratory for Turbulence and Complex System, Peking University, Beijing 100871, P. R. China

    Yi Peng Shi

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  1. Yi Peng Shi
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Correspondence to Yi Peng Shi.

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Shi, Y.P. Global Classical Solutions to the Equations of Two–dimensional MHD Transverse Flow. Acta Math Sinica 22, 1371–1384 (2006). https://doi.org/10.1007/s10114-005-0700-8

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  • DOI: https://doi.org/10.1007/s10114-005-0700-8

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