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

2011/12/06 by Killip, Rowan, Oh, Tadahiro, Pocovnicu, Oana +1 · 1 citation
#35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1112.1354

Abstract

We consider the Gross--Pitaevskii equation on \R⁴ and the cubic-quintic nonlinear Schrödinger equation (NLS) on \R³ 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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