We consider the energy-critical stochastic cubic nonlinear Schrödinger equation on R4 with additive noise, and with the non-vanishing boundary conditions at spatial infinity. By viewing this equation as a perturbation to the energy-critical cubic nonlinear Schrödinger equation on R4, we prove global well-posedness in the energy space. Moreover, we establish unconditional uniqueness of solutions in the energy space.
- Geometry and Topology
- Algebra and Number Theory