Well-Posedness results for non-isotropic perturbations of the nonlinear Schrödinger equation on cylindrical domains

Abstract: We consider a non-isotropically perturbed nonlinear Schrödinger equation posed on two-dimensional cylindrical domains of the form T×R T and R×T. This equation arises in models describing wave propagation in fiber arrays.

In this talk, we present several well-posedness results for initial data belonging to Sobolev spaces. For the cylindrical domain T×R, we establish global well-posedness in L^2xL^2 for small initial data by proving an L^4 – L^2 Strichartz-type inequality. In the case of the domain R×T, we were unable to adapt the same estimate, so we employed a different approach to obtain well-posedness for data with regularity above L^2 regularity.

Posted on Jun 16, 2025 in Differential Equations, Seminars