In the spring semester we will study some recent fluid dynamics related research papers, and later move to questions involving mixing. We will be meeting on Wednesdays at 3:30-5:30pm in B131. The currently scheduled talks are as follows:

1/30: Yao Yao	Kiselev, Nazarov, Volberg: Global well-posedness for the critical 2d dissipative quasi-geostrophic equation
2/6: Aaron Peterson	Cordoba, Cordoba, Fontelos: Formation of singularities for a transport equation with nonlocal velocity and Li, Rodrigo: Blow up of solutions for a 1D transport equation with nonlocal velocity and supercritical dissipation (continued on 2/13)
2/13: Xiao Xu	Dong, Du, Li: Finite time singularities and global well-posedness for fractal Burgers equations
2/20: Laura Cladek	Kiselev: Regularity and blow up for active scalars
2/27: Tam Do	Chae, Constantin, Cordoba, Gancedo, Wu: Generalized surface quasi-geostrophic equations with singular velocities
3/6: Jinsu Kim	Cordoba, Fefferman, de la Llave: On squirt singularities in hydrodynamics
3/13: Kyudong Choi	Denisov: The sharp corner formation in 2D Euler dynamics of patches: infinite double exponential rate of merging (continued on 3/20)
3/20: Taushean Lim	Cordoba, Fefferman: Growth of solutions for QG and 2D Euler equations
4/3: Vu Hoang	Nonexistence of bound states for a periodic waveguide problem
4/10: Yao Yao	Crippa, De Lellis: Estimates and regularity results for the DiPerna-Lions flow
4/17 & 4/24: Tam Do and Xiao Xu	Constantin, Kiselev, Ryzhik, Zlatoš: Diffusion and mixing in fluid flow
5/1: Kyudong Choi	Goudon, Poupaud: Homogenization of transport equations: A simple PDE approach to the Kubo formula
5/8: Diego Cordoba	Interface dynamics for incompressible fluids We consider the evolution of an interface generated between two immiscible, incompressible and irrotational fluids. Specifically we study the Muskat equation (the interface between oil and water in sand) and water wave equation (interface between water and vacuum). For both equations we will study well-posedness and the existence of smooth initial data for which the smoothness of the interface breaks down in finite time. We will also discuss some open problems.