Journal of the Mathematical Society of Japan

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

Kazuyoshi YOKOYAMA

Full-text: Open access

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: 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. Journal of the Mathematical Society of Japan 52 (2000), no. 3, 609--632. doi:10.2969/jmsj/05230609. http://projecteuclid.org/euclid.jmsj/1213107290.


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