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arXiv · 1501.05329

The nonlinear steepest descent method for Riemann-Hilbert problems of low regularity

Jonatan Lenells
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Abstract

We prove a nonlinear steepest descent theorem for Riemann-Hilbert problems with Carleson jump contours and jump matrices of low regularity and slow decay. We illustrate the theorem by deriving the long-time asymptotics for the mKdV equation in the similarity sector for initial data with limited decay and regularity.

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Jonatan Lenells. 2017-08-04. The nonlinear steepest descent method for Riemann-Hilbert problems of low regularity. https://arxiv.org/abs/1501.05329

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