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arXiv · 1510.00896

Sharp well-posedness for the Chen-Lee equation

Ricardo A. Pastrán R·Oscar G. Riaño C
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Abstract

We study the initial value problem associated to a perturbation of the Benjamin-Ono equation or Chen-Lee equation. We prove that results about local and global well-posedness for initial data in $H^s(R)$, with $s>-1/2$, are sharp in the sense that the flow-map data-solution fails to be $C^3$ in $H^s(\mathbb{R})$ when $s<-\frac{1}{2}$. Also, we determine the limiting behavior of the solutions when the dispersive and dissipative parameters goes to zero. In addition, we will discuss the asymptotic behavior (as $|x|\to \infty$) of the solutions by solving the equation in weighted Sobolev spaces.

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Ricardo A. Pastrán R, Oscar G. Riaño C. 2015-10-04. Sharp well-posedness for the Chen-Lee equation. https://arxiv.org/abs/1510.00896

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