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Scattering for the radial defocusing cubic nonlinear wave equation with initial data in the critical Sobolev space. (English) Zbl 1479.35549

Summary: We prove global well-posedness and scattering for the defocusing cubic nonlinear wave equation on \(\mathbb{R}^{1+3}\) with radial initial data lying in the critical Sobolev space \(\dot{H}^{1/2}(\mathbb{R}^3)\times\dot{H}^{-1/ 2}(\mathbb{R}^3)\). This result is sharp for radial initial data.

MSC:

35L15 Initial value problems for second-order hyperbolic equations
35L71 Second-order semilinear hyperbolic equations
35P25 Scattering theory for PDEs
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