| Abstract: |
| In this talk we discuss the solving of initial and boundary value problems for dispersive evolution equations. Models of such equations are the nonlinear Schr\odinger equation, the Korteweg-de Vries equation, and dispersive regularizations of Camassa-Holm type equations. For data in Sobolev spaces, we will present optimal well-posedness results based on sharp multilinear estimates motivated by estimating the solution of the forced linear problem in Bourgain solution spaces. Also, we shall present some implications of these estimates in the analytic theory of these equations. |
|