SPRING 2021 Nonlinear Analysis Seminar Series
Associate Professor Jean Van Schaftingen, Université catholique de Louvain
Title: Vortex dynamics for the lake equations
The lake equations describe the vertical average velocity in an inviscid incompressible flow of a fluid in a basin whose variable depth b : Ω →(0, +∞) is small in comparison with the size of its two-dimensional Ω⊂ℝ² projection. G. Richardson has showed by formal computations that vortices should at the leading order follow level lines of the depth function b. I will present different mathematical results showing the validity of this computation for stationary and time-dependent flows. These results are counterparts of classical results for the vortex dynamics of the Euler equation of inviscid incompressible flows.
This is joint work with Justin Dekeyser (UCLouvain, Louvain-la-Neuve, Belgium).