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

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 anadditional equation. With this new form, we obtain the local existence of smooth solution includingthe case that the initial density may tend to the vacuum state at infinity. Furthermore, the uniformlya priori estimation for the classical solutions is established and the global smooth solutions for a kindof initial data are obtained.