## Journal of the Mathematical Society of Japan

- J. Math. Soc. Japan
- Volume 52, Number 3 (2000), 609-632.

### Global existence of classical solutions to systems of wave equations with critical nonlinearity in three space dimensions

#### Abstract

We discuss the global existence of small solutions to the Cauchy problem for systems of quasilinear wave equations in three space dimensions, when their nonlinear terms have quadratic nonlinearity. A global existence theorem is established on the null condition which is extended to the condition for systems of wave equations with different propagation speeds.

#### Article information

**Source**

J. Math. Soc. Japan Volume 52, Number 3 (2000), 609-632.

**Dates**

First available in Project Euclid: 10 June 2008

**Permanent link to this document**

http://projecteuclid.org/euclid.jmsj/1213107290

**Digital Object Identifier**

doi:10.2969/jmsj/05230609

**Mathematical Reviews number (MathSciNet)**

MR1760608

**Zentralblatt MATH identifier**

0968.35081

**Subjects**

Primary: 35L05: Wave equation

Secondary: 35L15: Initial value problems for second-order hyperbolic equations 35L70: Nonlinear second-order hyperbolic equations

**Keywords**

Global existence Systems of wave equations Null conditions

#### Citation

YOKOYAMA, Kazuyoshi. Global existence of classical solutions to systems of wave equations with critical nonlinearity in three space dimensions. J. Math. Soc. Japan 52 (2000), no. 3, 609--632. doi:10.2969/jmsj/05230609. http://projecteuclid.org/euclid.jmsj/1213107290.