Electron. J. Diff. Equ., Vol. 2014 (2014), No. 158, pp. 1-10.

Cauchy problem for dispersive equations in alpha-modulation spaces

Qian Huang, Jiecheng Chen

In this article, we consider the Cauchy problem for dispersive equations in $\alpha$-Modulation spaces. For this purpose, we find a method for estimating $u^k$ in alpha-modulation spaces when k is not an integer, and develop a Strichartz estimate in $M_{p,q}^{s,\alpha}$ which is based on semigroup estimates. In the local case, we that the domain of p is independent of $\alpha$, which is also the case in the Modulation spaces and in the Besov space.

Submitted May 14, 2014. Published July 17, 2014.
Math Subject Classifications: 35A01, 35A02, 35L05.
Key Words: alpha-Modulation spaces; dispersive equation; Cauchy problem.

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Qiang Huang
Department of Mathematics, Zhejiang University
Hangzhou 310027, China
email: huangqiang0704@163.com
  Jiecheng Chen
Department of Mathematics, Zhejiang Normal University
Jinhua 321004, China
email: jcchen@zjnu.edu.cn

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