An initial boundary value problem for one-dimensional shallow water magnetohydrodynamics in the solar tachocline

In this article we investigate the shallow water magnetohydrodynamic equations in space dimension one with Dirichlet boundary conditions only for the velocity. This model has been proposed to study the phenomena in the solar tachocline. In this article, the local well-posedness in time of the model is proven by constructing the approximate solutions and showing the strong convergence of the approximate solutions.