Solitary water waves in finite and infinite depth

Solitary water waves in finite and infinite depth

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Miles Wheeler , New York University
Fine Hall 322

We will discuss the qualitative properties of spatially localized traveling water waves. First we will review some results for waves in a 2D finite-depth fluid with vorticity and possibly density stratification but no surface tension. Next we will consider waves in a 2D or 3D infinite-depth fluid with or without surface tension but with an irrotational velocity field. In this second case we prove asymptotic formulas for the velocity potential and free surface, and relate the constants in these formulas to the kinetic energy. As a consequence, we find that nontrivial waves must have infinite angular momentum. The first part includes joint work with Robin Ming Chen and Samuel Walsh, and also Walter Strauss.