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

Niklas Jöckel

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

Analysis of PDEs 2024-06-05 v3

Authors: Niklas Jöckel

Abstract

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 $H^s(\mathbb{R})+H^\sigma(\mathbb{T})$ for $s>\frac{1}{2}$ and $\sigma>\frac{7}{2}$ . These results follow by studying a generalized forced Benjamin-Ono equation.

Keywords

Benjamin-Ono equation local well-posedness bounded initial data periodic functions bore-like functions Sobolev spaces forced equation

Cite

@article{arxiv.2402.01464,
  title  = {Local well-posedness of the Benjamin-Ono equation for a class of bounded initial data},
  author = {Niklas Jöckel},
  journal= {arXiv preprint arXiv:2402.01464},
  year   = {2024}
}

Comments

56 pages. Corrected an error in Section 5.3 leading to $s>\frac{1}{2}$ instead of $s>\frac{1}{4}$ in Theorem 1.1

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