Well-posedness and Critical Index Set of the Cauchy Problem for the Coupled KdV-KdV Systems on $\mathbb{T}$

Xin Yang, Bing-Yu Zhang

Studied in this paper is the well-posedness of the Cauchy problem for the coupled KdV-KdV systems \[ u_t+a_1u_{xxx} = c_{11}uu_x+c_{12}vv_x+d_{11}u_{x}v+d_{12}uv_{x}, \quad u(x,0)=…