Instructor: Gene Wayne (MCS 242) The PDE Seminar this spring will focus on the fluid mechanical equations of interest in geophysics. The increasing interest in, and importance of, has lead to renewed study of the partial differential equations describing the oceans, atmosphere, and their interactions. This semester, I'll begin by deriving the Navier-Stokes and Euler equations (which describe respectively viscous and inviscid flows). We'll then talk about the effects of studying these equations in a rotating coordinate frame. Often the full equations are too difficult to understand and it may be appropriate to use approximations such as the quasi-geostrophic, hydrostatic, or two-dimensional approximations. We'll discuss how these approximations arise (non-rigorously). One possible topic for later in the semester is how one might justify these approximations analytically. We'll also look at some of the results on existence of solutions for these equations. Possible further topics, depending on the interest of the participants are point vortex models, more on approximate models for ocean or atmospheric flows, water waves and their approximations or special features of two-dimensional flows.

I'll keep an updated reading list on the course webpage.

Grading: All students enrolled in the course will be expected to give at least two lectures on topics related to the course. Your grade will be based on these lectures.