Well-posedness for a Family of Perturbations of the KDV Equation in Periodic Sobolev Spaces of Negative Order

Xavier Carvajal, Ricardo Pastran

We establish local well-posedness in Sobolev spaces $H^s(\mathbb{T})$, with $s\ge -1/2$, for the initial value problem issues of the equation $$ u_t + u_{xxx}+ηLu + uu_x=0;\; x\in…