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.