Abstract
We consider the defocusing mass-critical nonlinear Schr?dinger equation in the exterior domain in (). By analyzing Strichartz estimate and utilizing the inductive hypothesis method, we prove the stability for all initial data in .
Highlights
Our stability theorem concerns mass-critical stability in L2 (Ω) for the initial-value problem associated to the Equation (1)
We consider a mass-critical stability of the defocusing mass-critical nonlinear Schrödinger equation
We prove two different types of perturbation to show the stability of nonlinear Schrödinger equation
Summary
Gallouet [1] considered that iut − ∆u = −k u 2 u in Ω ×[0, ∞) , k ∈ , the nonlinear Schrödinger equation in Ω of a bounded domain or an exterior domain of 2 with Dirichlet boundary conditions. Tzvetkov described nonlinear Schrödinger equations in exterior domains. Schrödinger equation and the focusing cubic nonlinear Schrödinger equation in the exterior domain Ω of a smooth, compact, strictly convex obstacle in 3 with Dirichlet boundary conditions, respectively. Visan established stability of energy-critical nonlinear Schrödinger equations in d (d ≥ 3). Our stability theorem concerns mass-critical stability in L2 (Ω) for the initial-value problem associated to the Equation (1).
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