The authors establish global solutions to the energy-supercritical nonlinear wave equation in R^{1+3} for initial data that decomposes into a dispersed large-L2 piece and a localized short-pulse piece, yielding global existence in all homogeneous Sobolev norms.
A conformal-type energy inequality on hyperboloids and its application to quasi-linear wave equation in $\mathbb{R}^{3+1}$
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
In the present work, we will develop a conformal inequality in the hyperbolic foliation context which is analogous to the conformal inequality in the classical time-constant foliation context. Then as an application, we will apply this a priori estimate to the problem of global existence of quasi-linear wave equations in three spatial dimensions under null condition. With the aid of this inequality, we can establish more precise decay estimates on the global solution.
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math.AP 2verdicts
UNVERDICTED 2representative citing papers
Establishes global existence for a weakly coupled nonlinear wave-Klein-Gordon system in two spatial dimensions via conformal energy estimates on hyperboloids and normal form transforms.
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Global dynamics of a supercritical wave equation in a large data regime
The authors establish global solutions to the energy-supercritical nonlinear wave equation in R^{1+3} for initial data that decomposes into a dispersed large-L2 piece and a localized short-pulse piece, yielding global existence in all homogeneous Sobolev norms.
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Global solutions of nonlinear wave-Klein-Gordon system in two spatial dimensions: weak coupling case
Establishes global existence for a weakly coupled nonlinear wave-Klein-Gordon system in two spatial dimensions via conformal energy estimates on hyperboloids and normal form transforms.