|Date:||Mon, November 29, 2010|
|Place:||Research II Lecture Hall|
Abstract: In this talk I will give an introduction to gravity-capillary water waves. Such waves arise as critical points of a Hamiltonian H subject to an impulse constraint.
In particular, I will show that there exists a minimiser of H subject to the constraint I=2μ where μ is a small positive number. The existence of a solitary wave is thus assured, and since H and I are both conserved quantities its stability follows by a standard argument. `Stability' must however be understood in a qualified sense due to the lack of a global well-posedness theory for three-dimensional water waves.