The radial defocusing energy-supercritical NLS in dimension four

Abstract

We consider the radial defocusing nonlinear Schrödinger equations $i{u}_t+\Delta u=|u{|}^{p}u$ with supercritical exponent $p>4$ in four space dimensions, and prove that any radial solution that remains bounded in the critical Sobolev space must be global and scatter.

arXiv comment20 pages. arXiv admin note: text overlap with arXiv:1305.3993; substantial text overlap with arXiv:1401.4766 by other authors

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Cited by in corpus (4)

• Global well-posedness and scattering for the defocusing ${\dot{H}}^{\frac{1}{2}}$-critical nonlinear Schrödinger equation in ${\mathbb{R}}^2$
• The interctitical defocusing nonlinear Schrödinger equations with radial initial data in dimensions four and higher
• Numerical simulations for the energy-supercritical nonlinear wave equation
• On scattering for the defocusing high dimensional inter-critical NLS