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Dive into the research topics where Gabriela Planas is active.

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Featured researches published by Gabriela Planas.


Nonlinearity | 2006

Inviscid limits for the Navier–Stokes equations with Navier friction boundary conditions

Dragoş Iftimie; Gabriela Planas

We consider the Navier–Stokes equations with Navier friction boundary conditions and prove two results. First, in the case of a bounded domain we prove that weak Leray solutions converge (locally in time in dimension ≥3 and globally in time in dimension 2) as the viscosity goes to 0 to a strong solution of the Euler equations, provided that the initial data converge in L2 to a sufficiently smooth limit. Second, we consider the case of a half-space and anisotropic viscosities: we fix the horizontal viscosity, send the vertical viscosity to 0 and prove convergence to the expected limit system under a weaker hypothesis on the initial data.


Siam Journal on Mathematical Analysis | 2005

ON THE INVISCID LIMIT FOR TWO-DIMENSIONAL INCOMPRESSIBLE FLOW WITH NAVIER FRICTION CONDITION ∗

M. C. Lopes Filho; H. J. Nussenzveig Lopes; Gabriela Planas

In [Nonlinearity, 11 (1998), pp. 1625--1636], Clopeau, Mikelic, and Robert studied the inviscid limit of the two-dimensional incompressible Navier--Stokes equations in a bounded domain subject to Navier friction--type boundary conditions. They proved that the inviscid limit satisfies the incompressible Euler equations, and their result ultimately includes flows generated by bounded initial vorticities. Our purpose in this article is to adapt and, to some extent, simplify their argument in order to include pth power integrable initial vorticities, with p > 2.


Siam Journal on Mathematical Analysis | 2013

On the Nonhomogeneous Navier--Stokes System with Navier Friction Boundary Conditions

Lucas C. F. Ferreira; Gabriela Planas; Elder J. Villamizar-Roa

We address the issue of existence of weak solutions for the nonhomogeneous Navier--Stokes system with Navier friction boundary conditions allowing the presence of vacuum zones and assuming rough conditions on the data. We also study the convergence, as the viscosity goes to zero, of weak solutions for the nonhomogeneous Navier--Stokes system with Navier friction boundary conditions to the strong solution of the Euler equations with variable density, provided that the initial data converge in


Applicable Analysis | 2015

Existence of solutions for a class of Navier–Stokes equations with infinite delay

Sandro Marcos Guzzo; Gabriela Planas

L^{2}


Applied Mathematics Letters | 2019

Inviscid limit for SQG equation in different dispersive regimes via relative energy inequality

Leonardo Kosloff; Cesar J. Niche; Gabriela Planas

to a smooth enough limit.


Communications on Pure and Applied Analysis | 2018

Well-posedness for a non-isothermal flow of two viscous incompressible fluids

Juliana Honda Lopes; Gabriela Planas

In this paper, a class of Navier–Stokes equations with infinite delay is considered. It includes delays in the convective and the forcing terms. We discuss the existence of mild and classical solutions for the problem. We establish the results for an abstract delay problem by using the fact that the Stokes operator is the infinitesimal generator of an analytic semigroup of bounded linear operators. Finally, we apply these abstract results to our particular situation.


Nonlinear Analysis-real World Applications | 2012

Global attractor and omega-limit sets structure for a phase-field model of thermal alloys

Pedro Marín-Rubio; Gabriela Planas

Abstract We consider the dissipative surface quasigeostrophic equation with a dispersive forcing term and study the relation of solutions with vanishing viscosity to solutions of the inviscid equation with strong, constant or no dispersion. We show convergence by developing estimates based on the relative energy inequality.


Journal of Differential Equations | 2015

Mild solutions to the time fractional Navier-Stokes equations in R-N

Paulo Mendes de Carvalho-Neto; Gabriela Planas

This work is concerned with a non-isothermal diffuse-interface model which describes the motion of a mixture of two viscous incompressible fluids. The model consists of modified Navier-Stokes equations coupled with a phase-field equation given by a convective Allen-Cahn equation, and energy transport equation for the temperature. This model admits a dissipative energy inequality. It is investigated the well-posedness of the problem in the two and three dimensional cases without any restriction on the size of the initial data. Moreover, regular and singular potentials for the phase-field equation are considered.


arXiv: Analysis of PDEs | 2003

On the inviscid limit for 2D incompressible flow with Navier friction condition

M. C. Lopes Filho; H. J. Nussenzveig Lopes; Gabriela Planas

Abstract In this paper, the existence of weak solutions is established for a phase-field model of thermal alloys supplemented with Dirichlet boundary conditions. After that, the existence of global attractors for the associated multi-valued dynamical systems is proved, and the relationship among these sets is established. Finally, we provide a more detailed description of the asymptotic behaviour of solutions via the omega-limit sets. Namely, we obtain a characterization–through the natural stationary system associated to the model–of the elements belonging to the omega-limit sets under suitable assumptions.


Discrete and Continuous Dynamical Systems | 2008

Asymptotic behaviour of two-dimensional time-delayed Navier-Stokes equations

Eduardo Hernández; Gabriela Planas

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José Luiz Boldrini

State University of Campinas

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Cesar J. Niche

Federal University of Rio de Janeiro

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Sandro Marcos Guzzo

State University of West Paraná

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Lucas C. F. Ferreira

State University of Campinas

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M. C. Lopes Filho

State University of Campinas

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Franck Sueur

Centre national de la recherche scientifique

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