Preprint A263/2003
On the Cauchy problem for a coupled system of KdV equations
Mahendra Panthee | Linares, Felipe
Keywords: KdV equation | Cauchy problem
We study some questions related to the well-posedness for the initial value problem associated to the system $$\begin{cases} u_{t}+u_{xxx}+a_3v_{xxx}+uu_{x}+a_1vv_{x}+a_2(uv)_x =0,\\ b_1v_{t}+v_{xxx}+b_2a_3u_{xxx}+vv_{x}+b_2a_2uu_{x}+b_2a_1(uv)_x=0. \nonumber \end{cases}$$ Using recent methods, we prove a sharp local result in Sobolev spaces. We also prove global result under some conditions on the coefficients.