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arXiv · 1411.3535

Cauchy problem for NLKG in modulation spaces with noninteger powers

Huang Qiang·Fan Dashan·Chen Jiecheng
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Abstract

In this paper, we consider the Cauchy problem for the nonlinear Klein-Gordon equation whose nonlinearity is $|u|^{k}u$ in the modulation space, where $k$ is not an integer. Our method can be applied to other equations whose nonlinear parts have regularity estimates. We also study the global solution with small initial value for the Klein-Gordon-Hartree equation. By this we can show some advantages of modulation spaces both in high and low regularity cases.

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Huang Qiang, Fan Dashan, Chen Jiecheng. 2014-11-13. Cauchy problem for NLKG in modulation spaces with noninteger powers. https://arxiv.org/abs/1411.3535

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