Scattering theory for nonlinear Schrödinger equations with inverse-square potential

By Junyong Zhang, Jiqiang Zheng. 2013

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Abstract We study the long-time behavior of solutions to nonlinear Schrodinger equations with some critical rough potential of a | x | − 2 type. The new ingredients are the interaction Morawetz-type inequalities and Sobolev norm property associated with P a = − Δ + a | x | − 2 . We use such properties to obtain the scattering theory for the defocusing energy-subcritical nonlinear Schrodinger equation with inverse square potential in energy space H 1 ( R n ) .

Subfields: Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/76abb8795def2824871c77c28f5e32911e93d8dc