Duke Mathematical Journal

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

S. Klainerman and I. Rodnianski

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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

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

First available in Project Euclid: 26 May 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]


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. https://projecteuclid.org/euclid.dmj/1085598339

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