Steady waves in flows over periodic bottoms

CDSNS Colloquium
Friday, April 30, 2021 - 1:00pm for 1 hour (actually 50 minutes)
Zoom (see additional notes for link)
Carlos Garcia Azpeitia – UNAM – cgazpe@hotmail.com
Alex Blumenthal

Please Note: Zoom link:

In this talk we present the formation of steady waves in two-dimensional fluids under a current with mean velocity $c$ flowing over a periodic bottom. Using a formulation based on the Dirichlet-Neumann operator, we establish the unique continuation of a steady solution from the trivial solution for a flat bottom, with the exception of a sequence of velocities $c_{k}$.  Furthermore, we prove that at least two steady solutions for a near-flat bottom persist close to a non-degenerate $S^1$-orbit of steady waves for a flat bottom. As a consequence, we obtain the persistence of at least two steady waves close to a non-degenerate $S^1$-orbit of Stokes waves bifurcating from the velocities $c_{k}$ for a flat bottom. This is a joint work with W. Craig.