Global well-posedness of the 4-d energy-critical stochastic nonlinear Schrödinger equations with non-vanishing boundary condition

Abstract

We consider the energy-critical stochastic cubic nonlinear Schrödinger equation on ${\mathbb{R}}^4$ 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 ${\mathbb{R}}^4$, we prove global well-posedness in the energy space. Moreover, we establish unconditional uniqueness of solutions in the energy space.

18 pages. arXiv admin note: text overlap with arXiv:1904.06793, arXiv:1112.1354 by other authors

References in corpus (3)

• Travelling waves for the Gross-Pitaevskii equation II
• The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions
• On the stochastic nonlinear Schrödinger equations at critical regularities

Cited by in corpus (2)

• Global well-posedness of the energy-critical stochastic nonlinear wave equations
• Global well-posedness of the energy-critical stochastic Hartree nonlinear wave equation