The 3D Euler Equation

P. Constantin, D. Cordoba, C. Fefferman, Y. Sinai, and A. Shnirelman will be studying problems related to singular solutions of the (3-dimensional incompressible) Euler equation. Sinai plans to use methods from dynamical systems to look at possible singularities of the Euler and Navier-Stokes equations. Shnirelman will study generalized Euler solutions, including various notions of weak solutions, to try to continue Euler solutions past a singularity. Constantin, Cordoba, and Fefferman will look for rapid front formation in the quasi-geostrophic equation, in hopes of constructing solutions of the Euler equation with rapid vorticity growth. Our directions may change during the semester, but will stay focused on problems around singular solutions in fluid mechanics.