Mathematics > Analysis of PDEs
[Submitted on 16 Mar 2014]
Title:Scattering for a Nonlinear Schrödinger Equation with a Potential
View PDFAbstract:We consider a 3d cubic focusing nonlinear Schrödinger equation with a potential $$i\partial_t u+\Delta u-Vu+|u|^2u=0,$$ where $V$ is a real-valued short-range potential having a small negative part. We find criteria for global well-posedness analogous to the homogeneous case $V=0$ (Duyckaerts-Holmer-Roudenko). Moreover, by the concentration-compactness approach, we prove that if $V$ is repulsive, such global solutions scatter.
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