Existence for large times of strict solutions of nonlinear wave equations in three space dimensions for small initial data

Fritz John

Type: Article

Publication Date: 1987-01-01

Citations: 54

DOI: https://doi.org/10.1002/cpa.3160400104

View Publication

Locations

Communications on Pure and Applied Mathematics - View

Similar Works

Action	Title	Year	Authors
+	On the lifespan of solutions of nonlinear wave equations with small initial data	1990	Hans Lindblad
+	Lower bounds for the life span of solutions of nonlinear wave equations in three dimensions	1983	Fritz John
+	Global solutions of nonlinear hyperbolic equations for small initial data	1986	Demetrios Christodoulou
+	ON THE LARGE TIME BEHAVIOR OF SOLUTIONS TO SEMILINEAR SYSTEMS OF THE WAVE EQUATION	2009	Soichiro Katayama H. Kubo
+	Lower Bounds of the Life-Span of Small Classical Solutions for Nonlinear Wave Equations	1991	Tatsien Li
+	Uniform decay estimates and the lorentz invariance of the classical wave equation	1985	Sergiù Klainerman
+	Longtime existence for solutions of nonlinear wave equations with small initial data	1990	Fritz John
+ PDF Chat	Life-span of solutions to semilinear wave equation with time-dependent critical damping for specially localized initial data	2018	Masahiro Ikeda Motohiro Sobajima
+ PDF Chat	Global existence and blow-up for semilinear damped wave equations in three space dimensions	2019	Masakazu Kato Miku Sakuraba
+	NON-NEGATIVE SOLUTIONS OF THE CAUCHY PROBLEM FOR SEMILINEAR WAVE EQUATIONS AND NON-EXISTENCE OF GLOBAL NON-NEGATIVE SOLUTIONS	2009	Hiroshi Uesaka
+ PDF Chat	On the lifespan and the blowup mechanism of smooth solutions to a class of 2-D nonlinear wave equations with small initial data	2015	Bingbing Ding Ingo Witt Huicheng Yin
+	On the blowup and lifespan of smooth solutions to a class of 2-D nonlinear wave equations with small initial data	2015	Jun Li Ingo Witt Huicheng Yin
+	Life span of small solutions to a system of wave equations	2015	Kunio Hidano Kazuyoshi Yokoyama
+	Blow‐up for quasi‐linear wave equations in three space dimensions	1981	Fritz John
+	Almost global existence of elastic waves of finite amplitude arising from small initial disturbances	1988	Fritz John
+ PDF Chat	Life span of small solutions to a system of wave equations	2016	Kunio Hidano Kazuyoshi Yokoyama
+	On the critical decay and power for semilinear wave equtions in odd space dimensions	1996	Hideo Kubo
+	BLOWUP FOR SYSTEMS OF SEMILINEAR WAVE EQUATIONS WITH SMALL INITIAL DATA	2004	Xuwei
+	The lifespan of classical solutions to systems of nonlinear wave equations	2000	Hiroyuki Takamura
+	Global existence, asymptotic behaviour, and global non-existence of solutions for damped non-linear wave equations of Kirchhoff type in the whole space	2000	Kosuke Ono

Works That Cite This (52)

Action	Title	Year	Authors
+	Équations d'ondes quasilinéaires et estimations de Strichartz	1999	Hajer Bahouri Jean-Yves Chemin
+	Nonlinear Stability of Self-Gravitating Massive Fields	2024	Philippe G. LeFloch Yue Ma
+ PDF Chat	Global existence of classical solutions to systems of nonlinear wave equations with different speeds of propagation	2001	Kôji Kubota Kazuyoshi Yokoyama
+ PDF Chat	The lifespan of small solutions to cubic derivative nonlinear Schrödinger equations in one space dimension	2016	Yuji Sagawa Hideaki Sunagawa
+ PDF Chat	The hyperboloidal foliation method for nonlinear wave equations	2015	Philippe G. LeFloch Yue Ma
+ PDF Chat	The Rate of Convergence to the Asymptotics for the Wave Equation in an Exterior Domain	2010	Soichiro Katayama Hideo Kubo
+	Long time effects of nonlinearity in second order hyperbolic equations	1986	Fritz John
+ PDF Chat	LOWER BOUND OF THE LIFESPAN OF SOLUTIONS TO SEMILINEAR WAVE EQUATIONS IN AN EXTERIOR DOMAIN	2013	Soichiro Katayama Hideo Kubo
+	Global existence of null-form wave equations on small asymptotically Euclidean manifolds	2014	Chengbo Wang Xin Yu
+ PDF Chat	Small-data shock formation in solutions to 3D quasilinear wave equations: An overview	2016	Gustav Holzegel Sergiù Klainerman Jared Speck Willie Wai-Yeung Wong

Works Cited by This (9)

Action	Title	Year	Authors
+	The Cauchy problem for quasi-linear symmetric hyperbolic systems	1975	Tosio Kato
+	Blow‐up for quasi‐linear wave equations in three space dimensions	1981	Fritz John
+	Delayed singularity formation in solution of nonlinear wave equations in higher dimensions	1976	Fritz John
+	Uniform decay estimates and the lorentz invariance of the classical wave equation	1985	Sergiù Klainerman
+	Lower bounds for the life span of solutions of nonlinear wave equations in three dimensions	1983	Fritz John
+	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
+	Remarks on the global sobolev inequalities in the minkowski space R<sup>n+1</sup>	1987	Sergiù Klainerman
+	Long time effects of nonlinearity in second order hyperbolic equations	1986	Fritz John