Existence and Spectral Stability of Stokes Waves
In this talk we will give an overview of recent analytical and numerical results on the existence of periodic traveling wave solutions of the Euler equations of free-surface ideal fluid mechanics (the Stokes waves) and their dynamic stability. More specifically, we will show how "Boundary Perturbation Methods" can be used as effective tools in studying the Stokes waves and addressing the still open question of their dynamic stability. Portions of this are joint work with Fernando Reitich (Minnesota).