Well-posedness of the periodic dispersion-generalized Benjamin-Ono equation in the weakly dispersive regime

Niklas Jöckel

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arXiv · 2305.05638

Well-posedness of the periodic dispersion-generalized Benjamin-Ono equation in the weakly dispersive regime

Niklas Jöckel

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Abstract

We study the dispersion-generalized Benjamin-Ono equation in the periodic setting. This equation interpolates between the Benjamin-Ono equation ($\alpha=1$) and the viscous Burgers' equation ($\alpha=0$). We obtain local well-posedness in $H^s$ for $s>3/2-\alpha$ and $\alpha\in(0,1)$ by using the short-time Fourier restriction method.

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Niklas Jöckel. 2023-05-09. Well-posedness of the periodic dispersion-generalized Benjamin-Ono equation in the weakly dispersive regime. https://arxiv.org/abs/2305.05638

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