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arXiv · 1409.2381

On the propagation of regularities in solutions of the Benjamin-Ono equation

Pedro Isaza·Felipe Linares·Gustavo Ponce
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Abstract

We shall deduce some special regularity properties of solutions to the IVP associated to the Benjamin-Ono equation. Mainly, for datum $u_0\in H^{3/2}(\mathbb R)$ whose restriction belongs to $H^m((b,\infty))$ for some $m\in\mathbb Z^+,\,m\geq 2,$ and $b\in \mathbb R$ we shall prove that the restriction of the corresponding solution $u(\cdot,t)$ belongs to $H^m((β,\infty))$ for any $β\in \mathbb R$ and any $t>0$. Therefore, this type of regularity of the datum travels with infinite speed to its left as time evolves.

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Pedro Isaza, Felipe Linares, Gustavo Ponce. 2014-09-08. On the propagation of regularities in solutions of the Benjamin-Ono equation. https://arxiv.org/abs/1409.2381

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