Global Well-Posedness for Dissipative Korteweg-de Vries Equations

Abstract

This paper is devoted to the well-posedness for dissipative KdV equations u_t + u_xxx + |D_x|^2αu + uu_x = 0, 0 < α ≤ 1. An optimal bilinear estimate is obtained in Bourgain's type spaces, which provides global well-posedness in H^s(R), s > -3/4 for α ≤ 1/2 and s > -3/(5-2α) for α > 1/2.