Analysis Seminar

In this talk, we review recent progress on nonuniqueness and forward-in-time self-similar solutions of 2D Euler. Since Yudovich showed the uniqueness of weak solutions with L^1∩L^∞ vorticity for the 2D incompressible Euler equation, the nonuniqueness of solutions with L^1∩L^p was an open problem. Vishik proved the nonuniqueness of the forced equation while it is still unknown without forcing.

Besides, Bressan and Shen's numeric simulation demonstrates nonuniqueness in the class of self-similar solutions. However, even the presence of a self-similar solution is unknown except for a sufficiently small neighborhood of radial data which is proven by Elling and Shao-Wei-Zhang.