Global well-posedness and scattering for the defocusing mass-critical Schrödinger equation in the three-dimensional hyperbolic space

Source abstract

In this paper, we prove that the initial value problem for the mass-critical defocusing nonlinear Schrödinger equation on the three-dimensional hyperbolic space H 3 \mathbb {H}^3 is globally well-posed and scatters for data with radial symmetry in the critical space L 2 ( H 3 ) L^2 (\mathbb {H}^3) .