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# On the Cauchy Problem for Schrödinger-improved Boussinesq equations

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 Title: On the Cauchy Problem for Schrödinger-improved Boussinesq equations Authors: Ozawa, Tohru Browse this author Tsutaya, Kimitoshi Browse this author Issue Date: 2005 Publisher: Department of Mathematics, Hokkaido University Journal Title: Hokkaido University Preprint Series in Mathematics Volume: 740 Start Page: 1 End Page: 12 Abstract: The Cauchy problem for a coupled system of Schr\"odinger and improved Boussinesq equations is studied. Local well-posedness is proved in $L^2(\R^n)$ for $n\le 3$. Global well-posedness is proved in the energy space for $n\le 2$. Under smallness assumption on the Cauchy data, the local result in $L^2$ is proved for $n=4$. Type: bulletin (article) URI: http://hdl.handle.net/2115/69548 Appears in Collections: 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics