Water Waves: Breaking, Peaking and Disintegration

Abstract

Water waves describe the situation where water lies below a body of air and are acted on by gravity. Describing what we may see or feel at the beach or in a boat, they are a perfect example of applied mathematics. They encompass wide-ranging wave phenomena, from ripples driven by surface tension to tsunamis and to rogue waves. The interface between the water and the air is free and poses profound and subtle difficulties for rigorous analysis, numerical computation and modelling. In this lecture, the speaker will discuss some recent developments in the mathematical aspects of water wave phenomena. In particular, (1) is the solution to the Cauchy problem regular, or do singularities form after some time? (2) are there spatially periodic solutions? (3) and if so, are they stable?

About the speaker

Prof. Vera Mikyoung Hur received her PhD in Mathematics from Brown University in 2006. She joined the faculty of University of Illinois at Urbana-Champaign (UIUC) in 2009 and is currently the Professor of Mathematics and Associate Chair for Faculty.

Prof. Hur’s research puts together rigorous analysis, numerical computation, and modeling to address fundamental issues in the mathematical aspects of water waves. Particularly, she focuses on global regularity versus finite time singularities, the existence of traveling waves and their characterization, and the stability and instability of traveling waves.

Prof. Hur was elected the Simons Fellow in Mathematics (2016), the Beckman Fellow of Center for Advanced Study, UIUC (2014), and the Alfred P. Sloan Research Fellow (2012). She was also recipient of the Faculty Early Career Development (CAREER) Award of US National Science Foundation (2014).