# Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications

@article{Kenig2008NondispersiveRS, title={Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications}, author={Carlos E. Kenig and Carlos E. Frank Merle}, journal={American Journal of Mathematics}, year={2008}, volume={133}, pages={1029 - 1065} }

In this paper we establish optimal pointwise decay estimates for non-dispersive (compact) radial solutions to non-linear wave equations in 3 dimensions, in the energy supercritical range. As an application, we show for the full energy supercritical range, in the defocusing case, that if the scale invariant Sobolev norm of a radial solution remains bounded in its maximal interval of existence, then the solution must exist for all times and scatter.

## 120 Citations

### On the Energy Subcritical, Non-linear Wave Equation with Radial Data for $p\in (3,5)$

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### The radial defocusing energy-supercritical cubic nonlinear wave equation in

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We consider the defocusing nonlinear wave equation $u_{tt}-\Delta u + |u|^p u=0$ in the energy-supercritical regime p>4. For even values of the power p, we show that blowup (or failure to scatter)…

### Global Well-posedness for the Logarithmically Energy-Supercritical Nonlinear Wave Equation with Partial Symmetry

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### Scattering for defocusing energy subcritical nonlinear wave equations

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We consider the Cauchy problem for the defocusing power type nonlinear wave equation in $(1+3)$-dimensions for energy subcritical powers $p$ in the range $3 < p< 5$. We prove that any solution is…

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### Large Outgoing Solutions to Supercritical Wave Equations

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We prove the existence of global solutions to the energy-supercritical wave equation in R^{3+1}
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for a large class of radially…

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