Global well-posedness and scattering for the radial, defocusing, cubic wave equation with initial data in a critical Besov space

preprint2016arXivOpen access

Abstract

In this paper we prove that the cubic wave equation is globally well - posed and scattering for radial initial data lying in B1,12×B1,11B_{1,1}^{2} \times B_{1,1}^{1}. This space of functions is a scale invariant subspace of H˙1/2×H˙−1/2\dot{H}^{1/2} \times \dot{H}^{-1/2}.

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