14 papers
Mathematical study of a new Navier-Stokes-alpha model with nonlinear filter equation - Regularity theory and refined time asymptotics
Manuel Fernando Cortez, Oscar Jarrín
This article is devoted to the mathematical analysis of a new Navier--Stokes- model involving a nonlinear filter equation. The resulting model is governed by a doubly nonlinear…
On Stationary Gevrey Solutions to the Gravitational Boussinesq System and Applications to Uniqueness
Nestor Acevedo, Manuel Fernando Cortez, Oscar Jarrín
The stationary version of the Boussinesq system with a general gravitational acceleration term is considered. Under suitable assumptions on this term, as well as on the external fo…
Remarks on the Spatial Asymptotic Behavior of Solutions to a 1D Model of Equatorial Oceanic Flows
Manuel Fernando Cortez, Oscar Jarrin
We consider a new nonlocal and nonlinear one-dimensional evolution model arising in the study of oceanic flows in equatorial regions, recently derived in [A. Constantin and L. Moli…
Sharp Well-Posedness and Parameter Asymptotics for a Nonlocal Model of Thin Film Flows
Manuel Fernando Cortez, Oscar Jarrin, Miguel Yangari
This work focuses on the mathematical analysis of the Cauchy problem associated with a two-dimensional equation describing the dynamics of a thin fluid film flowing down an incline…
The role of the dimension in uniqueness results for the stationary quasi-geostrophic system
Diego Chamorro, Manuel Fernando Cortez
In this paper, we study a Liouville-type theorem for the stationary fractional quasi-geostrophic equation in various dimensions. Indeed, our analysis focuses on dimensions n = 2, 3…
Mathematical study of a new Navier-Stokes-alpha model with nonlinear filter equation -- Part I
Manuel Fernando Cortez, Oscar Jarrin
This article is devoted to the mathematical study of a new Navier-Stokes-alpha model with a nonlinear filter equation. For a given indicator function, this filter equation was firs…
Sharp well-posedness and spatial decaying for a generalized dispersive-dissipative Kuramoto-type equation and applications to related models
Manuel Fernando Cortez, Oscar Jarrin
We introduce a fairly general dispersive-dissipative nonlinear equation, which is characterized by fractional Laplacian operators in both the dispersive and dissipative terms. This…
On the long-time behavior for a damped Navier-Stokes-Bardina model
Manuel Fernando Cortez, Oscar Jarrín
In this paper, we consider a damped Navier-Stokes-Bardina model posed on the whole three-dimensional. These equations have an important physical motivation and they arise from some…
Spatial behavior of solutions for a large class of non-local PDE's arising from stratified flows
Manuel Fernando Cortez, Oscar Jarrin
We propose a theoretical model of a non-local dipersive-dissipative equation which contains as a particular case a large class of non-local PDE's arising from stratified flows. Wit…
On decay properties and asymptotic behavior of solutions to a non-local perturbed KdV equation
Manuel Fernando Cortez, Oscar Jarrín
We consider the \emph{KdV} equation with an additional non-local perturbation term defined through the Hilbert transform, also known as the OST-equation. We prove that the solution…
On the dynamics of zero-speed solutions for Camassa-Holm type equations
Miguel A. Alejo, Manuel F. Cortez, Chulkwang Kwak +1
In this paper we consider globally defined solutions of Camassa-Holm (CH) type equations outside the well-known nonzero speed, peakon region. These equations include the standard C…
Blowup issues for a class of nonlinear dispersive wave equations
Lorenzo Brandolese, Manuel Fernando Cortez
In this paper we consider the nonlinear dispersive wave equation on the real line, , that for appropri…
PDEs in Moving Time Dependent Domains
Manuel Fernando Cortez, Aníbal Rodríguez-Bernal
In this work we study partial differential equations defined in a domain that moves in time according to the flow of a given ordinary differential equation, starting out of a given…
On permanent and breaking waves in hyperelastic rods and rings
Lorenzo Brandolese, Manuel Fernando Cortez
We prove that the only global strong solution of the periodic rod equation vanishing in at least one point is the identically zero solution. Such conclusion holds provi…