Well-posedness of generalized KdV and one-dimensional fourth-order derivative nonlinear Schrödinger equations for data with an infinite $L^2$ norm

Abstract

We study the Cauchy problem for the generalized KdV and one-dimensional fourth-order derivative nonlinear Schrödinger equations, for which the global well-posedness of solutions with the small rough data in certain scaling limit of modulation spaces is shown, which contain some data with infinite $L^2$ norm.

17 pages, all comments are welcome

References in corpus (2)

• Wellposedness of Cauchy problem for the Fourth Order Nonlinear Schrödinger Equations in Multi-dimensional Spaces
• Well-posedness and scattering for fourth order nonlinear Schrödinger type equations at the scaling critical regularity