The energy-critical NLS with inverse-square potential

Abstract

We consider the defocusing energy-critical nonlinear Schrödinger equation with inverse-square potential $i{u}_t=-\Delta u+a|x{|}^{-2}u+|u{|}^{4}u$ in three space dimensions. We prove global well-posedness and scattering for $a>-\frac{1}{4}+\frac{1}{25}$. We also carry out the variational analysis needed to treat the focusing case.

References in corpus (4)

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Cited by in corpus (4)

• Minimal mass blow-up solutions for the $L^2$ critical NLS with inverse-square potential
• The focusing cubic NLS with inverse-square potential in three space dimensions
• Multi-center Vector Field Methods for Wave Equations
• Resolvent Estimates for the 3D Schrödinger Operator with Inverse-Square Potential