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

100%

Miao C. , Zhu Y.

2006

tom 89

nr 2

163-195

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.

Factorization theorem for product Hardy spaces

80%

Chen W. , Han Y. , Miao C.

nr 3

235-249

We extend the well known factorization theorems on the unit disk to product Hardy spaces, which generalizes the previous results obtained by Coifman, Rochberg and Weiss. The basic tools are the boundedness of a certain bilinear form on ℝ²₊ × ℝ²₊ and the characterization of BMO(ℝ²₊ × ℝ²₊) recently obtained by Ferguson, Lacey and Sadosky.