5 papers
Large data scattering for the defocusing -dispersion generalized Benjamin-Ono equation in the energy space
Luccas Campos, Felipe Linares, Thyago S. R. Santos
We study the defocusing -dispersion generalized Benjamin-Ono equation. For every even integer , we prove that solutions with initial data in the energy space $H^{\fracÎ…
Local existence of solutions and blow-up criteria for the Boussinesq equations in Lei-Lin-Gevrey Spaces
PatrÃcia L. Guidolin, Wilberclay G. Melo, Thyago S. R. Santos
This paper studies the local well-posedness and the behavior at potential finite blow-up times of mild solutions to the three-dimensional fractional Boussinesq equations in Lei-Lin…
Exponential blow-up of mild solutions to the fractional Boussinesq equations in the Gevrey class
Wilberclay G. Melo, Cilon Perusato, Thyago S. R. Santos
This work establishes conditions for the existence and uniqueness of local mild solutions to the Boussinesq equations with fractional dissipations in Sobolev-Gevrey spaces. We prov…
Small-amplitude self-similar solutions for one-dimensional nonlinear dispersive equations
Simão Correia, Gonçalo Pereira, Thyago S. R. Santos
Given a nonlinear dispersive equation which admits a scaling invariance, there may exist self-similar solutions. In this work, we present a systematic approach for the construction…
The Cauchy problem for nonlinear dispersive models of long internal waves in the presence of the Coriolis force
Ricardo Freire, Thyago S. R. Santos
We investigate models of dispersive long internal waves with rotational effects, specifically the Benjamin-Ono (BO) and intermediate long wave (ILW) equations modified by the prese…