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arXiv · 1912.05342

Long-time Asymptotic Behavior of the Fifth-order Modified KdV Equation in Low Regularity Spaces

Nan Liu·Mingjuan Chen·Boling Guo
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Abstract

Based on the nonlinear steepest descent method of Deift and Zhou for oscillatory Riemann--Hilbert problems and the Dbar approach, the long-time asymptotic behavior of solutions to the fifth-order modified Korteweg-de Vries equation on the line is studied in the case of initial conditions that belong to some weighted Sobolev spaces. Using techniques in Fourier analysis and the idea of $I$-method, we give its global well-posedness in lower regularity Sobolev spaces, and then obtain the asymptotic behavior in these spaces with weights.

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Nan Liu, Mingjuan Chen, Boling Guo. 2019-12-26. Long-time Asymptotic Behavior of the Fifth-order Modified KdV Equation in Low Regularity Spaces. https://arxiv.org/abs/1912.05342

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