Attractors for 2D-Navier–Stokes models with delays

T Caraballo, J Real - Journal of Differential Equations, 2004 - Elsevier
The existence of an attractor for a 2D-Navier–Stokes system with delay is proved. The theory
of pullback attractors is successfully applied to obtain the results since the abstract functional …

Invariant measures for the 3D globally modified Navier–Stokes equations with unbounded variable delays

J Wang, C Zhao, T Caraballo - Communications in Nonlinear Science and …, 2020 - Elsevier
This article investigates the three-dimensional globally modified Navier–Stokes equations
with unbounded variable delays. Firstly, we prove the global well-posedness of the …

Asymptotic behaviour of two–dimensional Navier–Stokes equations with delays

T Caraballo, J Real - Proceedings of the Royal Society of …, 2003 - royalsocietypublishing.org
Some results on the asymptotic behaviour of solutions to Navier–Stokes equations when the
external force contains some hereditary characteristics are proved. We show two different …

Mild solutions to time fractional stochastic 2D-Stokes equations with bounded and unbounded delay

J Xu, Z Zhang, T Caraballo - Journal of Dynamics and Differential …, 2022 - Springer
In this paper, the well-posedness of stochastic time fractional 2D-Stokes equations of order α
∈ (0, 1) α∈(0, 1) containig finite or infinite delay with multiplicative noise is established …

[HTML][HTML] Stability results for 2D Navier–Stokes equations with unbounded delay

L Liu, T Caraballo, P Marín-Rubio - Journal of Differential Equations, 2018 - Elsevier
Some results related to 2D Navier–Stokes equations when the external force contains
hereditary characteristics involving unbounded delays are analyzed. First, the existence and …

Pullback attractors for a two-dimensional Navier–Stokes model in an infinite delay case

P Marín-Rubio, J Real, J Valero - Nonlinear Analysis: Theory, Methods & …, 2011 - Elsevier
We prove the existence of solutions for a Navier–Stokes model in two dimensions with an
external force containing infinite delay effects in the weighted space Cγ (H). Then, under …

Pullback attractors for 2D Navier-Stokes equations with delays and their regularity

J García-Luengo, P Marín-Rubio… - Advanced Nonlinear …, 2013 - degruyter.com
In this paper we obtain some results on the existence of solution, and of pullback attractors,
for a 2D Navier-Stokes model with finite delay studied in [4] and [6]. Actually, we prove a …

[PDF][PDF] The exponential stability of neutral stochastic delay partial differential equations

T Caraballo, J Real, T Taniguchi - Discrete and …, 2007 - pdfs.semanticscholar.org
In this paper we analyse the almost sure exponential stability and ultimate boundedness of
the solutions to a class of neutral stochastic semilinear partial delay differential equations …

Method of Lyapunov functionals construction in stability of delay evolution equations

T Caraballo, J Real, L Shaikhet - Journal of Mathematical Analysis and …, 2007 - Elsevier
The investigation of stability for hereditary systems is often related to the construction of
Lyapunov functionals. The general method of Lyapunov functionals construction which was …

Attractors for 2D-Navier–Stokes equations with delays on some unbounded domains

P Marín-Rubio, J Real - Nonlinear Analysis: Theory, Methods & …, 2007 - Elsevier
We prove the existence of tempered and nontempered pullback attractors for two
dimensional Navier–Stokes equations on unbounded domains satisfying Poincaré …