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Global well-posedness and scattering for the radial, defocusing, cubic nonlinear wave equation

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arxiv 1809.08284 v1 pith:L3DJV7CF submitted 2018-09-21 math.AP

Benjamin Dodson This is my paper · ORCID
classification math.AP
keywords mathbfcubicdefocusingequationglobalnonlinearradialscattering
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abstract

In this paper we prove global well-posedness and scattering for the defocusing, cubic, nonlinear wave equation on $\mathbf{R}^{1 + 3}$ with radial initial data lying in the critical Sobolev space $\dot{H}^{1/2}(\mathbf{R}^{3}) \times \dot{H}^{-1/2}(\mathbf{R}^{3})$.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Global behaviors of defocusing semilinear wave equations

    math.AP 2019-08 conditional novelty 7.0 of 10

    Defocusing semilinear wave equations in dimension d at least 3 satisfy integrated local energy decay for all energy-subcritical and critical powers, and scatter for powers above 1 + sqrt(d^2 + 4d - 4) / (d - 1) withou...

  2. Scattering of solutions to NLW by Inward Energy Decay

    math.AP 2019-09 conditional novelty 6.0 of 10

    For radial finite-energy solutions of the 3D defocusing energy-subcritical nonlinear wave equation, decay of only the inward part of the energy implies forward scattering, and slightly faster decay gives explicit rates.

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