The mathematical study of water waves began with the derivation of the basic mathematical equations of any fluid by Euler in 1752. Later, water waves, which have a free boundary at the air interface, played a central role in the work of Poisson, Cauchy, Stokes, Levi-Civita and many others. In the last quarter century it has become a particularly active mathematical research area.

I will limit my discussion to classical 2D traveling water waves with vorticity. By means of local and global bifurcation theory using topological degree, we now know that there exist many such waves. They are exact smooth solutions of the Euler equations with the physical boundary conditions. Numerical computations provide insight into their properties. I will mention a number of properties that are the subjects of current research such as: their heights, their steepness, the possibility of self-intersection, and their stability or instability.

https://msu.zoom.us/j/98489542865
Meeting ID: 984 8954 2865
Passcode: 160185 Speaker(s): Walter Strauss (Brown University)