10 papers
Global well-posedness for the modified dispersion-generalized Benjamin-Ono equations
Mikaela Baldasso, Simão Correia, Thyago S. R. Santos
In this short note, we prove the global well-posedness of the modified dispersion-generalized Benjamin-Ono equation with dispersion , $$\partial_t u + D^α\partial_x u + u^2\…
Local well-posedness for the exponentially modified Benjamin-Ono equation
Thyago S. R. Santos
We prove local well-posedness for the modified Benjamin-Ono equation in for . This equation arises as a modified counterpart of the Benjamin-Ono equation t…
On solutions for damped fractional Navier-Stokes equations in a critical Lei-Lin-Gevrey space
Bruno S. Donato, Wilberclay G. Melo, Thyago S. R. Santos
We study the fractional Navier-Stokes equations with cubic damping in the specific Lei-Lin-Gevrey space (with and ). We establi…
Quantum communication and Bell nonlocality require infinite classical communication to simulate
Carlos de Gois, Thyago S. R. Santos, Carlos Vieira
A quantum system of any fixed dimension can be prepared in a continuum of states, yet it cannot be used to transmit an unlimited amount of classical information. Similarly, the cor…
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^{\fracα…
Local existence of solutions and blow-up criteria for the Boussinesq equations in Lei-Lin-Gevrey Spaces
Patrícia 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…
Sharp well-posedness for the -dispersion generalized Benjamin-Ono equations: Short and long time results
Luccas Campos, Felipe Linares, Thyago S. R. Santos
We consider the -dispersion generalized Benjamin-Ono (-DGBO) equations. For nonlinearities with power , we establish local and global well-posedness results for the…