arXiv subjects

Niklas Jöckel

Publications and source records attributed to Niklas Jöckel.

2 recordsLinked to original sources

arXiv2024

Local well-posedness of the Benjamin-Ono equation for a class of bounded initial data

We prove local well-posedness of the Benjamin-Ono equation for a class of bounded initial data including periodic and bore-like functions. As a consequence, we obtain local well-posedness in $H^s(\mathbb{R})+H^σ(\mathbb{T})$ for $s>\frac{1}{2}$ and $σ>\frac{7}{2}$. These results follow by studying a generalized forced Benjamin-Ono equation.

math.AP↗

arXiv2023

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

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

math.AP↗