Koç University, Mathematics Seminar

Date & Time: Friday, November 27, 14:00-15:00

Place: CAS Z-48

Speaker: Aynur Bulut (University of Michigan)

Title: Probabilistic Well-Posedness for Nonlinear Wave and Schrodinger Equations

Abstract: In this talk, we give an overview of several results on local and global in time well-posedness for the nonlinear wave and Schrodinger equations, with an emphasis on techniques which allow for treatment of initial data supercritical with respect to the scaling of the nonlinearity.  For this class of data, the initial value problems are ill-posed — uniform continuity of the solution map cannot hold — and we are therefore required to go beyond deterministic constructions based on fixed-point methods.  In particular, we consider the problems in a probabilistic setting, with randomized initial data, where the results are asked to hold for data occurring almost surely in the randomization — that is, excluding a measure zero set of initial data.  A careful choice of function spaces is combined with ideas coming from the study of finite dimensional Hamiltonian systems to produce a class of a priori bounds which hold in this probabilistic setting.  This is partially joint work with J. Bourgain.  The talk is intended to be self-contained, and to be accessible to graduate students. 

Speaker’s Homepage: http://www-personal.umich.edu/~abulut/