# 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);

 TeX DVI37Kb

## 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\$.

Item Type: Preprint 20 Schro"dinger equations, improved Boussinesq equation, Cauchy Problem 35-xx PARTIAL DIFFERENTIAL EQUATIONS 1055