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Title: Global Well-Posedness for the Defocusing, Cubic, Nonlinear Wave Equation in Three Dimensions for Radial Initial Data in $\dot{H}^{s} \times \dot{H}^{s - 1}$, $s> \frac{1}{2}$
Abstract In this paper we study the defocusing, cubic nonlinear wave equation in three dimensions with radial initial data. The critical space is $$\dot{H}^{1/2} \times \dot{H}^{-1/2}$$. We show that if the initial data is radial and lies in $$\left (\dot{H}^{s} \times \dot{H}^{s - 1}\right ) \cap \left (\dot{H}^{1/2} \times \dot{H}^{-1/2}\right )$$ for some $$s> \frac{1}{2}$$, then the cubic initial value problem is globally well-posed. The proof utilizes the I-method, long time Strichartz estimates, and local energy decay. This method is quite similar to the method used in [11].  more » « less
Award ID(s):
1500424
PAR ID:
10156295
Author(s) / Creator(s):
Date Published:
Journal Name:
International Mathematics Research Notices
Volume:
2019
Issue:
21
ISSN:
1073-7928
Page Range / eLocation ID:
6797 to 6817
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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