On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles

Authors:
Kunio Hidano, Jason Metcalfe, Hart F. Smith, Christopher D. Sogge and Yi Zhou

Journal:
Trans. Amer. Math. Soc. **362** (2010), 2789-2809

MSC (2000):
Primary 35L05, 35L20, 35L71

DOI:
https://doi.org/10.1090/S0002-9947-09-05053-3

Published electronically:
December 8, 2009

MathSciNet review:
2584618

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Abstract | References | Similar Articles | Additional Information

Abstract: We establish the Strauss conjecture concerning small-data global existence for nonlinear wave equations, in the setting of exterior domains to compact obstacles, for space dimensions and . The obstacle is assumed to be nontrapping, and the solution is assumed to satisfy either Dirichlet or Neumann conditions along the boundary of the obstacle. The key step in the proof is establishing certain ``abstract Strichartz estimates'' for the linear wave equation on exterior domains.

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Additional Information

**Kunio Hidano**

Affiliation:
Department of Mathematics, Mie University, Mie Prefecture, Japan

**Jason Metcalfe**

Affiliation:
Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599-3260

**Hart F. Smith**

Affiliation:
Department of Mathematics, University of Washington, Seattle, Washington 98195-4350

**Christopher D. Sogge**

Affiliation:
Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21244

**Yi Zhou**

Affiliation:
School of Mathematical Science, Fudan University, Shanghai, People’s Republic of China

DOI:
https://doi.org/10.1090/S0002-9947-09-05053-3

Received by editor(s):
February 13, 2009

Published electronically:
December 8, 2009

Additional Notes:
The first author was supported in part by the Grant-in-Aid for Young Scientists (B) (No. 18740069), The Ministry of Education, Culture, Sports, Science and Technology, Japan, and he would like to thank the Department of Mathematics at the Johns Hopkins University for the hospitality and financial support during his visit where part of this research was carried out

The second, third and fourth authors were supported by the National Science Foundation

The fifth author was supported by project 10728101 of NSFC and the “111” project and Doctoral Programme Foundation of the Ministry of Education of China.

Article copyright:
© Copyright 2009
American Mathematical Society

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