Continuous Dependence of Cauchy Problem For Nonlinear Schrödinger Equation in H^s

2010/09/10 by Wei Dai, Weihua Yang, Dai, Wei +3
Mathematics · Physics and Astronomy · #35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP #msc:35Q55

paper · pdf · doi:10.48550/arxiv.1009.2005

48pages, no figure. arXiv admin note: text overlap with arXiv:1006.2745 by other authors

arxiv created 2012/02/10 · arxiv updated 2012/02/13

Abstract

We consider the Cauchy problem for the nonlinear Schrödinger equation i ∂_tu+ Δu=λ₀u+λ₁|u|^αu in ℝ^N, where λ₀,λ₁∈ℂ, in H^s subcritical and critical case: 0<α≤(4)/(N-2s) when 1<s<(N)/(2) and 0<α<+∞ when s≥(N)/(2). We show that the solution depends continuously on the initial value in the standard sense in H^s(ℝ^N) if α satisfies certain assumptions.

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