The paper “Singular limits of the shallow water equations on the sphere“, co-authored by Bin Cheng and Steve Schochet (Tel-Aviv University), has been accepted for publication in the SIAM J Mathematical Analysis (SIMA). In the paper, solutions of the slightly compressible shallow water equations on a rapidly rotating sphere are shown to be bounded uniformly when ratio of the Froude number to the Rossby number is bounded. Moreover, in the singular limit in which the ratio of those parameters remains fixed while they both tend to zero, solutions with well-prepared initial data tend to corresponding solutions of limit equations. A link to the final-form arXiv version is here. There are three key theorems in the paper, and a screenshot of the first is shown below.