On the Cauchy Problem for Schro"dinger-improved Boussinesq equations
Preprint Series # 740
Ozawa, Tohru and Tsutaya, Kimitoshi On the Cauchy Problem for Schro"dinger-improved Boussinesq equations. (2005);
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 $n=4$.
|Uncontrolled Keywords:||Schro"dinger equations, improved Boussinesq equation, Cauchy Problem |
|Subjects:||35-xx PARTIAL DIFFERENTIAL EQUATIONS|