### Steady waves in flows over periodic bottoms

- Series
- CDSNS Colloquium
- Time
- Friday, April 30, 2021 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Zoom (see additional notes for link)
- Speaker
- Carlos Garcia Azpeitia – UNAM – cgazpe@hotmail.com

**Please Note:** Zoom link: https://zoom.us/j/97732215148?pwd=Z0FBNXNFSy9mRUx3UVk4alE4MlRHdz09

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.