# American Institute of Mathematical Sciences

June  2005, 4(2): 209-240. doi: 10.3934/cpaa.2005.4.209

## Global solutions of the wave-Schrödinger system with rough data

 1 Mathematical Institute, Tohoku University, Sendai 980-8578, Japan

Received  January 2004 Revised  December 2004 Published  March 2005

We prove that the wave-Schröodinger system is globally well-posed for data in $(H^{s_{1}} \times \dot{H}^{s_{2}} \times \dot{H}^{s_{2}-1})(\mathbb^{d})$, where $d=3,4$ and $s_{1},s_{2}> q_{d} \ (q_{3}=(\sqrt{57}-5)/4, \ q_{4}=\sqrt{3}-1)$. Our proof is based on the I-method. We introduce the space $\Omega^{s,b}$ which controls the low frequency part and the modified multiplier for I-method to work in the space $\Omega^{s,b}$.
Citation: Takafumi Akahori. Global solutions of the wave-Schrödinger system with rough data. Communications on Pure & Applied Analysis, 2005, 4 (2) : 209-240. doi: 10.3934/cpaa.2005.4.209
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