The defocusing energy-supercritical nonlinear wave equation in three space dimensions

Authors:
Rowan Killip and Monica Visan

Journal:
Trans. Amer. Math. Soc. **363** (2011), 3893-3934

MSC (2010):
Primary 35L71

DOI:
https://doi.org/10.1090/S0002-9947-2011-05400-0

Published electronically:
January 28, 2011

MathSciNet review:
2775831

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We consider the defocusing nonlinear wave equation in the energy-supercritical regime . For even values of the power , we show that blowup (or failure to scatter) must be accompanied by blowup of the critical Sobolev norm. An equivalent formulation is that solutions with bounded critical Sobolev norm are global and scatter. The impetus to consider this problem comes from recent work of Kenig and Merle who treated the case of spherically-symmetric solutions.

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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

DOI:
https://doi.org/10.1090/S0002-9947-2011-05400-0

Received by editor(s):
January 22, 2010

Received by editor(s) in revised form:
June 14, 2010

Published electronically:
January 28, 2011

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.