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

Journal of the Mathematical Society of Japan

Volumn 52, Issue 3, 2000, Pages 609-632

  Yokoyama, Kazuyoshi ^a  

^a HOKKAIDO UNIVERSITY   (Japan)

Author keywords

Global existence; Null conditions; Systems of wave equations

Indexed keywords

EID: 0001321428     PISSN: 00255645     EISSN: 18811167     Source Type: Journal    
DOI: 10.2969/jmsj/05230609     Document Type: Article

References (11)

1. R. Agemi and K. Yokoyama, The null condition and global existence to the system of wave equations with different speeds, Advances in Nonlinear Partial Differential Equations and Stochastics, Series on Advances in Mathematics for Applied Sciences, 48 (edited by S. Kawashima and T. Yanagisawa), World Scientific, 1998, 43-86.
2. B. Hanouzet and J.-L. Joly, Applications bilinéaires compatibles avec un opérateur hyperbolique, Ann. Inst. Henri Poincaré-Analyse Non Linéaire, 4, 1987, 357-376.
3. A. Hoshiga and H. Kubo, Global small amplitude solutions of nonlinear hyperbolic systems with a critical exponent under the null condition, preprint.
4. F. John, Lower bounds for the life span of solutions of nonlinear wave equations in three space dimensions, Comm. Pure Appl. Math., 36, 1983, 1-35.
5. F. John, Nonlinear wave equations, Formation of singularities, Pitcher lectures in the Math. Sci., Lehigh Univ., American Math. Soc., 1990.
6. T. Kato, The Cauchy problem for quasi-linear symmetric hyperbolic systems, Arch. Rational Mech. Anal., 58, 1975, 181-205.
7. 1 estimates for solutions to the classical wave equation in three space dimensions, Comm. Pure Appl. Math., 37, 1984, 269-288.
8. S. Klainerman, The null condition and global existence to nonlinear wave equations, Lectures in Appl. Math., 23, 1986, Amer. Math. Soc., 293-326.
9. S. Klainerman and T. C. Sideris, On almost global existence for nonrelativistic wave equations in 3D, Comm. Pure Appl. Math., 49, 1996, 307-321.
10. M. Kovalyov, Resonance-type behaviour in a system of nonlinear wave equations, J. Differential Equations, 77, 1989, 73-83.
11. A. Majda, Compressible fluid flow and systems of conservation laws in several space variables, Springer.