Singularity formation and stability issues arising in water waves


Date
07/19/2015 - 07/31/2015
Location
CAMP
Research Background and Goal We plan to discuss recent developments in the theory of equations that arise as models for fluid motion. The research in this area has been carried on by groups that have largely focused upon only one type of equation. Considering the progress that has been made as well as the recalcitrance of some of the open issues, it seems timely to bring together successful workers on the various equations of fluid motion for an extended discussion of issues and methods. This includes the Quasi-Geostrophic equations with their non-local dissipation. This model arises in atmospheric and oceanic science. Benjamin-Ono-type equations and their relatives have also seen extended mathematical development recently. Main Information A particular focus of the conversation will be on models that feature non-local operators. The discussion is envisioned to deal with fundamental issues of local existence and regularity, but interest will devolve more to issues of singularity formation. Research Expected Effect Considering the progress that has been made as well as the recalcitrance of some of the open issues, it seems timely to bring together successful workers on the various equations of fluid motion for an extended discussion of issues and methods. Especially mixing people who are numerically based with theoreticians seems propitious. Research Expected Result We shall derive new class of water waves models and shw the existence of certain types of solutions such as solitary waves and periodic waves.