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

Details Continuous Dependence of Cauchy Problem For Nonlinear Schrödinger Equation in $H^{s}$ Continuous Dependence of Cauchy Problem For Nonlinear Schrödinger Equation in $H^{s}$

2010-09-10

arxiv.org/abs/1009.2005v4

Mathematics

Analysis of PDEs

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

Scientific paper

We consider the Cauchy problem for the nonlinear Schr\"{o}dinger equation $i \partial_{t}u+ \Delta u=\lambda_{0}u+\lambda_{1}|u|^\alpha u$ in $\mathbb{R}^{N}$, where $\lambda_{0},\lambda_{1}\in\mathbb{C}$, in $H^s$ subcritical and critical case: $0<\alpha\leq\frac{4}{N-2s}$ when $1

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