The Cauchy problem for the coupled Klein-Gordon-Schrödinger system

• Autorzy: Changxing Miao , Youbin Zhu
• Języki publikacji: EN

Abstrakty

EN

We consider the Cauchy problem for a generalized Klein-Gordon-Schrödinger system with Yukawa coupling. We prove the existence of global weak solutions by the compactness method and, through a special choice of the admissible pairs to match two types of equations, we prove the uniqueness of those solutions by an approach similar to the method presented by J. Ginibre and G. Velo for the pure Klein-Gordon equation or pure Schrödinger equation. Though it is very simple in form, the method has an unnatural restriction on the power of interactions. In the last part of this paper, we use special admissible pairs and Strichartz estimates to remove the restriction, thereby generalizing previous results and obtaining the well-posedness of the system.

Kategorie tematyczne

• 35L15: Initial value problems for second-order hyperbolic equations
• 35L05: Wave equation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2006
• Tom: 89
• Numer: 2
• Strony: 163-195

Daty

wydano

2006

Twórcy

autor

Changxing Miao

• Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China

autor

Youbin Zhu

• Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China

Identyfikatory

DOI

10.4064/ap89-2-6