Global solutions of the Klein-Gordon-Schrödinger system with rough data. (English) Zbl 1164.35511

Pecher, Hartmut

Differ. Integral Equ. 17, No. 1-2, 179-214 (2004).

Summary: The Klein-Gordon-Schrödinger system with Yukawa coupling is shown to have a unique global solution for rough data, which do not necessarily have finite energy. The proof uses a generalized bilinear estimate of Strichartz type and Bourgain’s idea to split the data into low- and high-frequency parts.

MSC:

35Q99

Partial differential equations of mathematical physics and other areas of application

Keywords:

Klein-Gordon-Schrödinger system; Yukawa coupling; unique global solution