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arXiv · 2211.05329

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

Yufeng Lu
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Abstract

We study the Cauchy problem for the generalized KdV and one-dimensional fourth-order derivative nonlinear Schr\"odinger 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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Yufeng Lu. 2022-11-10. Well-posedness of generalized KdV and one-dimensional fourth-order derivative nonlinear Schr\"odinger equations for data with an infinite $L^2$ norm. https://doi.org/10.1111/sapm.12559

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