Global solutions of non-linear wave-Klein-Gordon system in two space dimension: semi-linear interactions

Abstract

In this work we consider the problem of global existence of small regular solutions to a type nonlinear wave-Klein-Gordon system with semi-linear interactions in two spatial dimension. We develop some new techniques on both wave equations and Klein-Gordon equations in order to get sufficient decay rates when energies are not uniformly bounded. These techniques are compatible with those introduced in previous work on two spatial-dimensional quasi-linear wave-Klein-Gordon systems, and can be applied in much general cases.

arXiv comment29 pages

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Cited by in corpus (8)

• Asymptotic Behavior of the Solution to the Klein-Gordon-Zakharov Model in Dimension Two
• Global solution to the wave and Klein-Gordon system under null condition in dimension two
• Almost global well-posedness for quasilinear strongly coupled wave-Klein-Gordon systems in two space dimensions
• Two dimensional wave--Klein-Gordon equations with semilinear nonlinearities
• Global well-posedness for a system of quasilinear wave equations on a product space
• Global solutions of non-linear wave-Klein-Gordon system in one space dimension
• Global existence for systems of nonlinear wave and Klein-Gordon equations in two space dimensions under a kind of the weak null condition
• Remarks on basic calculus in hyperboloidal foliation