On the existence of global smooth solutions of certain semi-linear hyperbolic equations

1979 ◽  
Vol 167 (2) ◽  
pp. 99-135 ◽  
Author(s):  
Philip Brenner
Keyword(s):  
Hyperbolic Equations ◽  
Smooth Solutions ◽  
Global Smooth Solutions ◽  
Linear Hyperbolic Equations

Fast high order ADER schemes for linear hyperbolic equations

2004 ◽  
Vol 197 (2) ◽  
pp. 532-539 ◽  
Author(s):  
Thomas Schwartzkopff ◽  
Michael Dumbser ◽  
Claus-Dieter Munz
Keyword(s):  
Hyperbolic Equations ◽  
High Order ◽  
Linear Hyperbolic Equations

Singularities of solutions for first order quasilinear hyperbolic systems

1983 ◽  
Vol 94 (1-2) ◽  
pp. 137-147 ◽  
Author(s):  
Lee Da-tsin(Li Ta-tsien) ◽  
Shi Jia-hong
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Hyperbolic Systems ◽  
Smooth Solutions ◽  
Small Initial Data ◽  
Quasilinear Hyperbolic Systems ◽  
First Order ◽  
Global Smooth Solutions ◽  
The Cauchy Problem

SynopsisIn this paper, the existence of global smooth solutions and the formation of singularities of solutions for strictly hyperbolic systems with general eigenvalues are discussed for the Cauchy problem with essentially periodic small initial data or nonperiodic initial data. A result of Klainerman and Majda is thus extended to the general case.

Global smooth solutions to 3D irrotational Euler equations for Chaplygin gases

2020 ◽  
Vol 17 (03) ◽  
pp. 613-637
Author(s):  
Changhua Wei ◽  
Yu-Zhu Wang
Keyword(s):  
Euler Equations ◽  
Compressible Euler Equations ◽  
Wave System ◽  
Smooth Solutions ◽  
Small Perturbations ◽  
Global Smooth Solutions ◽  
Compressible Euler ◽  
The Cauchy Problem ◽  
Constant State ◽  
New Formulation

We study here the Cauchy problem associated with the isentropic and compressible Euler equations for Chaplygin gases. Based on the new formulation of the compressible Euler equations in J. Luk and J. Speck [The hidden null structure of the compressible Euler equations and a prelude to applications, J. Hyperbolic Differ. Equ. 17 (2020) 1–60] we show that the wave system satisfied by the modified density and the velocity for Chaplygin gases satisfies the weak null condition. We then prove the global existence of smooth solutions to the irrotational and isentropic Chaplygin gases without introducing a potential function, when the initial data are small perturbations to a constant state.

Sign in / Sign up

Export Citation Format

Share Document