ESAIM: Proceedings and Surveys (Jan 2018)
Remark on the well-posedness of weakly dispersive equations
Abstract
We improve the results about the well-posedness of the regularized fractional dispersive equation (1 + Dxα)ut + ux + uux = 0 when 0 < α ≤ 1. When #x03B1; < 1, the existence and uniqueness of vanishing viscosity solution is proved.