EWM-EMS Summer School: Water Waves and Nonlinear Dispersive Equations
May 27 - May 31, 2024
During the last decades, nonlinear dispersive equations received a great deal of attention from mathematicians, partially due to ubiquitous applications in e.g., fluid dynamics, optics, and electromagnetics, but also due to its intrinsic mathematical beauty. The interplay between nonlinear and dispersive effects leads to the appearance of various wave phenomena, which range from smooth solutions and stability to singularity formations, blow-up, and instabilities. A particularly challenging topic in mathematics is the water-wave problem. Even under the simplest assumptions on the fluid, a complete understanding of all arising phenomena is largely missing, and many interesting problems remain open. Zooming in on certain regimes, such as shallow or deep water, one can derive nonlinear dispersive water-wave model equations. A rigorous qualitative study of their solutions leads to a better understanding of the water-wave problem and to deeper insights into ocean dynamics and their impact on global climate phenomena. Therefore, water-wave models lie on the border between pure and applied mathematics, and have applications to problems of great societal interest, such as climate studies.
The aim of the summer school is to introduce graduate students and postdoctoral fellows to fundamental concepts and current challenges in nonlinear PDEs appearing in the study of waters waves and nonlinear dispersive equations. The focus of the school will be on steady periodic solutions, stability analysis, and numerics for solutions with rough initial data.