Duke Mathematical Journal

Improved local well-posedness for quasilinear wave equations in dimension three

S. Klainerman and I. Rodnianski

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Abstract

We improve recent results of H. Bahouri and J.-Y. Chemin and of D. Tataru concerning local well-posedness theory for quasilinear wave equations. Our approach is based on the proof of the Strichartz estimates using a combination of geometric methods and harmonic analysis. The geometric component relies on and takes advantage of the nonlinear structure of the equation.

Article information

Source
Duke Math. J. Volume 117, Number 1 (2003), 1-124.

Dates
First available in Project Euclid: 26 May 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1085598339

Digital Object Identifier
doi:10.1215/S0012-7094-03-11711-1

Mathematical Reviews number (MathSciNet)
MR1962783

Zentralblatt MATH identifier
1031.35091

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 35L15: Initial value problems for second-order hyperbolic equations 58J45: Hyperbolic equations [See also 35Lxx]

Citation

Klainerman, S.; Rodnianski, I. Improved local well-posedness for quasilinear wave equations in dimension three. Duke Math. J. 117 (2003), no. 1, 1--124. doi:10.1215/S0012-7094-03-11711-1. http://projecteuclid.org/euclid.dmj/1085598339.


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References

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