MÁRQUEZ DURÁN , Antonio Miguel

We first study the existence and uniqueness of strong solutions of a three dimensional system of globally modified Navier-Stokes equations with finite delay in the locally Lipschitz case. The asymptotic behaviour of solutions, and the existence of pullback attractor are also analyzed.

"Como es bien conocido, las ecuaciones de Navier-Stokes gobiernan el movimiento de fluidos comunes como el agua, el aire, el aceite, etc. No es objeto de nuestra Memoria el estudio de tales ecuaciones, sujeto de innumerables trabajos matemáticos desde la aparición del primer artículo de Leray. La segunda parte de la misma es una continuación...

A nonclassical nonautonomous diffusion equation with delay is analyzed. First, we prove the existence and uniqueness of solutions by using the Galerkin approximations and the energy method. Next, we prove the existence and eventual uniqueness of stationary solutions, as well as their exponential stability. We emphasize that the assumptions...

En esta comunicación demostramos que, bajo ciertas hipótesis, de una sucesión de soluciones del modelo Navier-Stokes Globalmente Modificado con retardo podemos extraer una subsucesión que converge en un sentido adecuado a una solución débil del correspondiente modelo de Navier-Stokes en dimensión tres. También se analiza el caso en el que...

In this paper we consider a non-autonomous Navier-Stokes-Voigt model including a variety of delay terms in a unified formulation. Firstly, we prove the existence and uniqueness of solutions by using a Galerkin scheme. Next, we prove the existence and eventual uniqueness of stationary solutions, as well as their exponential stability by using...

Existence and uniqueness of solution for a globally modified version of Navier-Stokes equations containing infinite delay terms are established. Moreover, we also analyze the stationary problem and, under suitable additional conditions, we obtain global exponential decay of the solutions of the evolutionary problem to the stationary solution.

We prove that under suitable assumptions, from a sequence of solutions of globally modified Navier-Stokes equations with delays we can extract a subsequence which converges in an adequate sense to a weak solution of a three-dimensional Navier-Stokes equation with delays. An additional case with a family of different delays involved in the...

The long-time behaviour of a stochastic 3D LANS-® model on a bounded domain is analysed. First, we reformulate the model as an abstract problem. Next, we establish sufficient conditions ensuring the existence of stationary (steady state) solutions of this abstract nonlinear stochastic evolution equation, and study the stability properties of...

Existence and uniqueness of solution for a globally modified version of Navier-Stokes equations containing infinite delay terms are established. Moreover, we also analyze the stationary problem and, under suitable additional conditions, we obtain global exponential decay of the solutions of the evolutionary problem to the stationary solution.

Existence, uniqueness, and continuity properties of solutions for a globally modified version of Navier–Stokes equations with finite delay terms within a locally Lipschitz operator are established. Moreover, we also analyze the stationary problem, and, under suitable assumptions, we prove that there exists a unique stationary solution, which is...

We analyse the asymptotic behaviour of a 3D Lagrangian averaged Navier-Stokes -model (3D LANS) with delays. In fact, we apply the theory of pullback attractors to ensure the existence of a pullback attractor, and at the same time, we also prove the existence of a uniform (forward) attractor in the sense of Chepyzhov and Vishik. Instead of...

We obtain some results on the existence and uniqueness, and exponential stability of solutions for the three-dimensional ®¡Navier-Stokes model with delays, when the forcing term containing the delay is sub-linear and locally Lipschitz continuous.

Existence and uniqueness of solutions for a stochastic version of the 3D-Lagrangian averaged Navier-Stokes (LANS-®) equation in a bounded domain and containing some hereditary characteristics are proved.

In this paper, it is analyzed a non-classical non-autonomous di_usion equation with delay. First, the well-posedness and the existence of a local solution is proved by using a _xed point theorem. Then, the existence of solutions de_ned globally in future is ensured. The asymptotic behaviour of solutions is analyzed within the framework of...

We show existence and uniqueness of solutions for a non-classical and non-autonomous diffusion equation with infinite delay terms, analyzing the asymptotic behaviour in the pullback sense and obtaining global exponential decay to stationary solutions.

Durante el presente curso 2009/2010 la Universidad Pablo de Olavide (UPO), de Sevilla, ha puesto en marcha el nuevo mapa de titulaciones adaptado al Espacio Europeo de Educación Superior (EEES), el cual está compuesto por 16 grados y 6 dobles grados. Hasta llegar a este punto la UPO trabajó duro durante más de 6 años en la adaptación de su...