## Osaka Journal of Mathematics

### Global small amplitude solutions to systems of nonlinear wave equations with multiple speeds

#### Abstract

We give a global existence theorem to systems of quasilinear wave equations in three space dimensions, especially for the multiple-speed cases. It covers a wide class of quadratic nonlinearities which may depend on unknowns as well as their first and second derivatives. Our proof is achieved through total use of pointwise and $L^2$-estimates concerning unknowns and their first and second derivatives.

#### Article information

Source
Osaka J. Math., Volume 43, Number 2 (2006), 283-326.

Dates
First available in Project Euclid: 6 July 2006

https://projecteuclid.org/euclid.ojm/1152203942

Mathematical Reviews number (MathSciNet)
MR2262337

Zentralblatt MATH identifier
1195.35225

#### Citation

Katayama, Soichiro; Yokoyama, Kazuyoshi. Global small amplitude solutions to systems of nonlinear wave equations with multiple speeds. Osaka J. Math. 43 (2006), no. 2, 283--326. https://projecteuclid.org/euclid.ojm/1152203942

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