Nikolaos Tzirakis

In this talk I will discuss smoothing estimates for nonlinear dispersive equations that are posed on bounded or semi-infinite domains. The smoothing and decay properties of linear dispersive equations are well known. We examine how these properties carry over into their nonlinear perturbations. Applications of our smoothing estimates include almost everywhere convergence of the solution to the initial data, growth of Sobolev norms, dispersive quantization of periodic solutions, the structure of the attracting sets for dissipative dispersive PDE and uniqueness of solutions for initial-boundary value problems on the half-line. This is joint work with B. Erdogan and E. Compaan.