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January/February 2012 Some new well-posedness results for the Klein-Gordon-Schrödinger system
Hartmut Pecher
Differential Integral Equations 25(1/2): 117-142 (January/February 2012). DOI: 10.57262/die/1356012829


We consider the Cauchy problem for the 2D and 3D Klein-Gordon Schrödinger system. In 2D we show local well posedness for Schrödinger data in $H^s$ and wave data in $H^{\sigma} \times H^{\sigma -1}$ for $s=-1/4 \, +$ and $\sigma = -1/2$, whereas ill posedness holds for $s < - 1/4$ or $\sigma < -1/2$, and global well-posedness for $s\ge 0$ and $s-\frac{1}{2} \le \sigma < s+ \frac{3}{2}$. In 3D we show global well posedness for $s \ge 0$, $ s - \frac{1}{2} < \sigma \le s+1$. Fundamental for our results are the studies by Bejenaru, Herr, Holmer and Tataru [2], and Bejenaru and Herr [3] for the Zakharov system, and also the global well-posedness results for the Zakharov and Klein-Gordon-Schrödinger system by Colliander, Holmer and Tzirakis [5].


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Hartmut Pecher. "Some new well-posedness results for the Klein-Gordon-Schrödinger system." Differential Integral Equations 25 (1/2) 117 - 142, January/February 2012.


Published: January/February 2012
First available in Project Euclid: 20 December 2012

zbMATH: 1249.35309
MathSciNet: MR2906550
Digital Object Identifier: 10.57262/die/1356012829

Primary: 35L70 , 35Q55

Rights: Copyright © 2012 Khayyam Publishing, Inc.

Vol.25 • No. 1/2 • January/February 2012
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