Global well-posedness of the Gross--Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions

Details Global well-posedness of the Gross--Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions Global well-posedness of the Gross--Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions

2011-12-06

arxiv.org/abs/1112.1354v1

Mathematics

Analysis of PDEs

Scientific paper

We consider the Gross--Pitaevskii equation on $\R^4$ and the cubic-quintic nonlinear Schr\"odinger equation (NLS) on $\R^3$ with non-vanishing boundary conditions at spatial infinity. By viewing these equations as perturbations to the energy-critical NLS, we prove that they are globally well-posed in their energy spaces. In particular, we prove unconditional uniqueness in the energy spaces for these equations.

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