The well posedness of the dissipative Korteweg–de Vries equations with low regularity data Original Research Article

We study the Cauchy problem of a dissipative version of the KdV equation with rough initial data. By working in a Bourgain type space we prove the local and global well posedness results for Sobolev spaces of negative order, and the order number is lower than the well known value View the MathML source−34. In some sense this paper is intended to show how the Bourgain type space is applicable to the study of semilinear equations with a linear part which contain both dissipative and dispersive terms.