Global existence of small amplitude solutions to nonlinear coupled wave-Klein-Gordon systems in four space-time dimension with hyperboloidal foliation method

2011/05/20 by MA, Yue
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1105.4137

Abstract

In this article one will develop a new type of energy method based on a foliation of spacetime into hyperboloidal hypersurfaces . As we will see, with this method, some classical results such as global existence and almost global existence of regular solutions to the quasi-linear wave equations and Klein-Gordon equations will be established in a much simpler and much more natural way. Most importantly, the global existence of regular solutions to a general type of coupled quasilinear wave-Klein-Gordon system will be established. All of this suggests that compared with the classical method, this hyperboloidal foliation of space-time may be a more natural way to regard the wave operator.

Related

• Global existence of small amplitude solution to nonlinear system of wave\n and Klein-Gordon equations in four space-time dimensions
• Global solutions of non-linear wave-Klein-Gordon system in one space dimension
• The hyperboloidal foliation method
• Global solutions of nonlinear wave-Klein-Gordon system in two spatial dimensions: weak coupling case
• A non-linear damping structure and global stability of wave-Klein-Gordon coupled system in ℝ³⁺¹