Random data Cauchy problem for supercritical Schrödinger equations
Realizing vector fields without loss of derivatives
Recent progress in attractors for quintic wave equations
We report on new results concerning the global well-posedness, dissipativity and attractors for the quintic wave equations in bounded domains of with damping terms of the form , where or . The main ingredient of the work is the hidden extra regularity of solutions that does not follow from energy estimates. Due to the extra regularity of solutions existence of a smooth attractor then follows from the smoothing property when . For existence of smooth attractors is more complicated and follows...
Relativity and irreversibility.
Representation theorem for stochastic differential equations in Hilbert spaces and its applications.
Rigidity results for Bernoulli actions and their von Neumann algebras
Using very original methods from operator algebras, Sorin Popa has shown that the orbit structure of the Bernoulli action of a property (T) group, completely remembers the group and the action. This information is even essentially contained in the crossed product von Neumann algebra. This is the first von Neumann strong rigidity theorem in the literature. The same methods allow Popa to obtain II factors with prescribed countable fundamental group.
Rigorous numerics for the Cahn-Hilliard equation on the unit square.