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Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case. (English) Zbl 0958.35126

Summary: We establish global wellposedness and scattering for the \(H^{1}\)-critical defocusing nonlinear Schrödinger equation in 3D \[ iu_{t}+\Delta u - u|u|^{4}=0 \] assuming radial data \(\phi \in H^{s}\), \(s\geq 1\). In particular, it proves global existence of classical solutions in the radial case. The same result is obtained in 4D for the equation \[ iu_{t}+\Delta u -u|u|^{2} =0 . \]

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35L15 Initial value problems for second-order hyperbolic equations
Full Text: DOI

References:

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