On almost global existence for nonrelativistic wave equations in 3D

1996/03/01 by Sergiu Klainerman, Sergiù Klainerman, Thomas C. Sideris · 18 citations
Mathematics · Engineering · #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations #Computational Fluid Dynamics and Aerodynamics

paper · doi:10.1002/(sici)1097-0312(199603)49:3<307::aid-cpa4>3.0.co;2-h

Abstract

Almost global solutions are constructed to three-dimensional, quadratically nonlinear wave equations. The proof relies on generalized energy estimates and a new decay estimate. The method applies to equations that are only classically invariant, such as the nonlinear system of hyperelasticity. © 1996 John Wiley & Sons, Inc.

Citations

• Uniform decay estimates and the lorentz invariance of the classical wave equation

Cited by

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• Global Well-posedness of Incompressible Elastodynamics in Two Dimensions
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• Low regularity ill-posedness for elastic waves driven by shock formation
• A Morawetz type energy estimate for wave equation in ℝ² and application to elastic waves
• Global multidimensional shock waves for 2-D and 3-D unsteady potential flow equations
• Decay estimates of wave equations in un-isotropic media
• Space-Time resonances and the null condition for (first order) systems\n of wave equations

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