Nonlinear Schrödinger type system with quadratic interaction on Zoll manifolds

online | | 11:00

Mahendra Panthee

Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas, São Paulo, Brasil

In this talk, we consider the initial value problem (IVP) associated to a system consisting of nonlinear Schrödinger type equations with quadratic interaction posed on Zoll manifolds of dimension d  2 We derive some bilinear estimates in the associated Bourgain's space and prove the local well-posedness results for data with low order Sobolev regularity. We also use a Gagliardo-Nirenberg type inequality and conservation laws to prove that the local solution can be extended globally in time whenever s 1 in dimensions 2 and 3.

Joint work with Dr. Marcelo Nogueira.

Zoom link

Research Groups