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math.AP2019
Vortex motion for the lake equations
Justin Dekeyser, Jean Van Schaftingen
The lake equations $$\left\{\begin{aligned} \nabla \cdot \big( b \, \mathbf{u}\big) &= 0 & & \text{on}\ \mathbb{R}\times D,\\ \partial_t\mathbf{u} + (\mathbf{u}\cdot \nabla)\mathbf…
math.AP2017
Desingularization of a steady vortex pair in the lake equation
Justin Dekeyser
We construct a family of steady solutions of the lake model perturbed by some small Coriolis force, that converge to a singular vortex pair. The desingularized solutions are obtain…