The HADES seminar on Tuesday, September 13th will be at 3:30 pm in Room 740.

Speaker: James Rowan

Abstract:The existence of solitary waves has been a key question for mathematical models of water waves since the 1830s. The model I will discuss is the infinite depth, gravity, zero surface tension case in the presence of nonzero constant vorticity, a model that applies in settings with countercurrents. Because the infinite depth gravity water waves equations with constant vorticity are well-approximated (on a suitable timescale) by the Benjamin-Ono equation, which has solitary waves, one might expect a solitary wave to exist. We show that this is indeed the case, and that this wave is close to the solitary wave for the Benjamin-Ono soliton. This work is joint with Lizhe Wan.