Global well - posedness for the defocusing, cubic, nonlinear wave equation in three dimensions for radial initial in H^s × H^{s - 1}, s > (1)/(2)

2015/06/20 by Benjamin Dodson, Dodson, Benjamin
Mathematics · Physics and Astronomy · Engineering · #Advanced Mathematical Physics Problems #Nonlinear Waves and Solitons #Computational Fluid Dynamics and Aerodynamics

paper · pdf · doi:10.48550/arxiv.1506.06239

Abstract

In this paper we study the defocusing, cubic nonlinear wave equation in three dimensions with radial initial data. The critical space is H^1/2 × H^-1/2. We show that if the initial data is radial and lies in (H^s × H^{s - 1}) ∩ (H^1/2 × H^-1/2) for some s > (1)/(2), then the cubic initial value problem is globally well - posed. We use the I - method and the long time Strichartz estimates. This method is quite similar to the method used in [D2].

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