Scattering theory for nonlinear Schr?dinger equations with inverse-square potential
We study the long-time behavior of solutions to nonlinear Schrödinger 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 Pa = −Δ + a|x|−2. We use such properties to obtain the scattering theory for the defocusing energysubcritical nonlinear Schrödinger equation with inverse square potential in energy space H1(Rn).
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|Source:||Journal of Functional Analysis|
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