Hokkaido Mathematical Journal

AKAHORI Takafumi,

Global solutions of the wave-Schr\"odinger system below $L^{2}$.

Hokkaido Mathematical Journal, 35 (2006) pp.779-813

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Abstract

We prove that the 3 dimensional wave-Schr\"odinger system is globally well-posed for data in $(H^{s_{1}}\times \dot{H}^{s_{2}} \times \dot{H}^{s_{2}-1})(\R^{3})$, where both $s_{1}$ and $s_{2}$ are some negative indices.

MSC(Primary)35Q55
MSC(Secondary)
Uncontrolled Keywordsglobal well-posedness, wave-Schr\"odinger system