Speaker: Oscar Riano, Department of Mathematics and Statistics, FIU

Title: Well-posedness in weighted spaces for the generalized Hartree equation with nonlinearity p<2.

Abstract: 

The study of the competition between dispersive and nonlinearity effects has developed a wide range of questions and applications. In general, the dispersion is fixed, and a variable nonlinearity is considered. An inherent problem in this approach is the study of nonlinearities that involve low regularity, where usually the classical methods of existence cannot be applied directly. In this talk, we will discuss some applications of the approach proposed by Cazenave and Naumkin for the Schrodinger equation, in which the existence of solutions for nonlinearities with low regularity is proved by considering a class of initial data with a certain polynomial behavior. We will focus on the generalized Hartree equation with nonlinearities p<2, and use weighted estimates for the Riesz transform, as well as apply the fractional weights; this is the first such approach. This is a joint work with Anudeep K. Arora (University of Illinois at Chicago) and Svetlana Roudenko (FIU).