Scattering theory for the defocusing 3d NLS in the exterior of a
strictly convex obstacle
Scattering theory for the defocusing 3d NLS in the exterior of a
strictly convex obstacle
In this paper, we investigate the global well-posedness and scattering theory for the defocusing nonlinear Schr\"odinger equation $iu_t + \Delta_\Omega u = |u|^\alpha u$ in the exterior domain $\Omega$ of a smooth, compact and strictly convex obstacle in $\mathbb{R}^3$.It is conjectured that in Euclidean space, if the solution has a …