An initial-boundary value problem for the two-dimensional rotating shallow water equations with axisymmetry

Abstract

This paper is concerned with an initial-boundary value problem for the two-dimensional axisymmetric rotating shallow water equations. The Dirichlet boundary conditions are imposed only on the radial velocity, while no boundary condition is imposed on the height of the fluid or the angular velocity. A series of a priori estimates for the solution of the approximate linear problem are derived and the strong convergence of the approximate solution sequences is verified. Consequently, we establish the local well-posedness in time of strong solutions for the initial-boundary value problem of the model.