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

preprint2022arXivOpen access

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.

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

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Well-posedness of generalized KdV and one-dimensional fourth-order derivative nonlinear Schrödinger equations for data with an infinite L2L^2L2 norm

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