Water waves with density stratification or localized vorticity

Abstract: This talk will serve as a general introduction to two areas of active research in water waves. In the ocean, the presence of salt and temperature gradients can lead to substantial stratification of the density. This phenomenon is well-known to have significant physical implications. Indeed, it makes possible enormous ``internal waves'' that can dwarf even the largest waves seen on the surface. We will present an overview of the mathematical work on this subject, focusing primarily on recent results regarding the existence of large-amplitude solitary stratified waves.

The second part of the talk will discuss waves with localized distributions of vorticity. These include water waves with submerged point vortices, dipoles, vortex patches, and those exhibiting a vortex spike.

This is joint work with Robin Ming Chen, Mats Ehrnström, Jalal Shatah, Kristoffer Varholm, Erik Wahlén, Miles H. Wheeler, and Chongchun Zeng.

analysis of PDEsclassical analysis and ODEs

Audience: researchers in the topic

Online Northeast PDE and Analysis Seminar