Professor Walter Strauss
DEPARTMENT OF MATHEMATICS; BROWN UNIVERSITY
Steady Rotational Water Waves
Precise study of water waves began with the derivation of the basic mathematical equations of fluids by the great Euler in 1752. In the two and a half centuries since then, the theory of fluids has played a central role in the development of mathematics. Water waves are fluids with a free surface. I will discuss waves that travel at a constant speed. Using local and global bifurcation theory, we now know how to prove that there exist very many such waves. They may have either small or large amplitudes. I will outline the existence proof and then exhibit some recent computations of the waves using numerical continuation. The computations illustrate certain relationships between the amplitude, energy and mass flux of the waves. If the vorticity is sufficiently large, the first stagnation point of the wave occurs either at the crest, on the bed directly below the crest, or in the interior of the fluid. This work is a perfect example of the synergy between theory and computation.