## The radial defocusing energy-supercritical nonlinear wave equation in all space dimensions

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- by Rowan Killip and Monica Visan PDF
- Proc. Amer. Math. Soc.
**139**(2011), 1805-1817 Request permission

## Abstract:

We consider the defocusing nonlinear wave equation $u_{tt}-\Delta u + |u|^p u=0$ with spherically-symmetric initial data in the regime $\frac 4{d-2}<p<\frac 4{d-3}$ (which is energy-supercritical) and dimensions $3\leq d\leq 6$; we also consider $d\geq 7$, but for a smaller range of $p>\frac 4{d-2}$. The principal result is that blowup (or failure to scatter) must be accompanied by blowup of the critical Sobolev norm. An equivalent formulation is that maximal-lifespan solutions with bounded critical Sobolev norm are global and scatter.## References

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## Additional Information

**Rowan Killip**- Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095-1555
**Monica Visan**- Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095-1555
- Received by editor(s): February 8, 2010
- Received by editor(s) in revised form: May 26, 2010
- Published electronically: November 1, 2010
- Additional Notes: The first author was supported by NSF grant DMS-0701085

The second author was supported by NSF grant DMS-0901166 - Communicated by: Hart F. Smith
- © Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**139**(2011), 1805-1817 - MSC (2010): Primary 35L71
- DOI: https://doi.org/10.1090/S0002-9939-2010-10615-9
- MathSciNet review: 2763767