The energy-critical NLS with inverse-square potential

C. Miao; J. Zhang; J. Zheng; M. Visan; R. Killip

arxiv: 1509.05822 · v1 · pith:OSRHAON7new · submitted 2015-09-18 · 🧮 math.AP

The energy-critical NLS with inverse-square potential

R. Killip , C. Miao , M. Visan , J. Zhang , J. Zheng This is my paper

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keywords energy-criticalinverse-squarepotentialanalysiscarrycaseconsiderdefocusing

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We consider the defocusing energy-critical nonlinear Schr\"odinger equation with inverse-square potential $iu_t = -\Delta u + a|x|^{-2}u + |u|^4u$ in three space dimensions. We prove global well-posedness and scattering for $a>-\frac14 +\frac1{25}$. We also carry out the variational analysis needed to treat the focusing case.

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The energy-critical NLS with inverse-square potential

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