Global Solutions of Quasilinear Wave Equations

Hans Lindblad

Type: Article

Publication Date: 2008-02-01

Citations: 95

DOI: https://doi.org/10.1353/ajm.2008.0009

Abstract

We show global small data existence for a class of quasilinear wave equations related to Einstein's equations in harmonic coordinates. These equations do not satisfy the classical null condition and the asymptotic behavior of solutions is not free but the light cones bend at infinity.

Locations

American Journal of Mathematics - View
arXiv (Cornell University) - View - PDF

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Works Cited by This (12)

Action	Title	Year	Authors
+	The lifespan of classical solutions of non-linear hyperbolic equations	1987	Lars Hörmander
+	Blow‐up for quasi‐linear wave equations in three space dimensions	1981	Fritz John
+	On the lifespan of solutions of nonlinear wave equations with small initial data	1990	Hans Lindblad
+ PDF Chat	The weak null condition for Einstein's equations	2003	Hans Lindblad Igor Rodnianski
+ PDF Chat	Global Existence for the Einstein Vacuum Equations in Wave Coordinates	2005	Hans Lindblad Igor Rodnianski
+	Almost global existence to nonlinear wave equations in three space dimensions	1984	Franklin John Sergiù Klainerman
+	Global solutions of nonlinear hyperbolic equations for small initial data	1986	Demetrios Christodoulou
+	Global solutions of nonlinear wave equations	1992	Hans Lindblad
+ PDF Chat	Counterexamples to local existence for quasilinear wave equations	1998	Hans Lindblad
+	None	2000	Serge Alinhac