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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Ming Chen
University of Pittsburgh
Title: Existence of large-amplitude solitary stratified water waves

Abstract: We consider two-dimensional gravity solitary water waves with heterogeneous density. The presence of stratification allows for a wide variety of traveling waves, including fronts, so-called generalized solitary waves with ripples in the far field, and even fronts with ripples! Among these many possible wave patterns, we prove that for any smooth choice of upstream velocity and monotone streamline density function, there always exists a continuous curve of solitary waves with large amplitude, which are even and decreasing monotonically on either side of a central crest. As one moves along this curve, the horizontal fluid velocity comes arbitrarily close to the wave speed.

The construction of such solutions is achieved after proving symmetry results, bounds on the velocity field, and after ruling out the existence of monotone fronts. This is joint work with Samuel Walsh and Miles Wheeler.

Recording: http://mm.math.cmu.edu/recordings/cna/ming_chen_small.mp4
Date: Tuesday, March 1, 2016
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  Ian Tice