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Germán Fonseca

Publications and source records attributed to Germán Fonseca.

4 recordsLinked to original sources
arXiv2026

Decay and regularity properties for the dispersion generalized Benjamin-Ono equation

We study spatial decay properties of solutions to the dispersion generalized Benjamin-Ono equation. We first establish persistence properties in weighted Sobolev spaces under a sharp condition between decay and regularity, improving previous results. Additionally, extending recent works on the Benjamin-Ono equation by Linares and Ponce [27], we also show that decay at two distinct times implies additional regularity of solutions. The proof relies on weighted energy estimates and pseudo-differential methods, which build on an iterative mechanism that trades decay for regularity.

math.AP↗
arXiv2018

The IVP for a nonlocal perturbation of the Benjamin-Ono equation in classical and weighted Sobolev spaces

We prove that the initial value problem associated to a nonlocal perturbation of the Benjamin-Ono equation is locally and globally well-posed in Sobolev spaces $H^s(\mathbb{R})$ for any $s>-3/2$ and we establish that our result is sharp in the sense that the flow map of this equation fails to be $C^2$ in $H^s(\mathbb{R})$ for $s<-3/2$. Finally, we study persistence properties of the solution flow in the weighted Sobolev spaces $Z_{s,r}=H^s(\mathbb{R})\cap L^2(|x|^{2r}\,dx)$ for $s\geq r >0$. We also prove some unique continuation properties of the solution flow in these spaces.

math.AP↗
arXiv2013

Well-posedness results for the dispersion generalized Benjamin-Ono equation via the contraction principle

We study the initial value problem associated to the dispersion generalized Benjamin-Ono equation. Our aim is to establish well-posedness results in weighted Sobolev spaces via contraction principle under minimal requirements in the weighted order of the space. One of our new main ideas is the deduction of a pointwise estimate concerning the group describing the solution of the linear problem and the fractional weights.

math.AP↗