3 p.m. - 4 p.m. Location: SLC 1.202
Miles H. Wheeler
Courant Institute of Mathematical Sciences
New York University
Solitary water waves
The water wave equations describe the motion of a fluid (water) bounded above by a free surface. This free surface is subject to a constant (atmospheric) pressure, while gravity acts as an external force. Traveling waves which are localized (solitary) and have small amplitude can be described by models such as the Korteweg–de Vries equation. To investigate their large-amplitude cousins, however, it is necessary to work with the full (Euler) equations. In this talk we will use continuation arguments to construct curves of large-amplitude solitary waves. We will also prove several properties of solitary waves, for instance that they travel faster than the critical speed appearing in the Korteweg–de Vries approximation. The talk will include some joint work with Robin Ming Chen and Samuel Walsh, and also Walter Strauss.
Sponsored by the Department of Mathematical Sciences