Analysis and PDE Seminar: The Lake Equations with an Evanescent or Emerging Island

Speaker: Evelyne Miot

We study the asymptotical dynamics of the lake equations in case of vanishing or emerging of an island. We derive an asymptotic lake-type equation for both scenarios. In the first case, the asymptotic dynamics displays an additional Dirac mass in the vorticity. The main mathematical difficulty is that the equations are singular when the water depth vanishes. We provide new uniform estimates in weighted spaces for the related stream functions in order to obtain a compactness result. This is joint work with Lars Eric Hientzsch and Christophe Lacave (Université Grenoble Alpes).