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Global solutions of the wave-Schrödinger system with rough data

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  • 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 $\Omega^{s,b}$.
    Mathematics Subject Classification: 35L05,35Q55.

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