Stabilization of 3D Navier–Stokes–Voigt equations

AbstractWe consider 3D Navier–Stokes–Voigt equations in smooth bounded domains with homogeneous Dirichlet boundary conditions. First, we study the existence and exponential stability of strong stationary solutions to the problem. Then we show that any unstable steady state can be exponentially stabilized by using either an internal feedback control with a support large enough or a multiplicative Itô noise of sufficient intensity.

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The Pullback Asymptotic Behavior of the Solutions for 2D NonautonomousG-Navier-Stokes Equations

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.10-m1071 ◽

2012 ◽

Vol 4 (2) ◽

pp. 223-237 ◽

Cited By ~ 1

Author(s):

Jinping Jiang ◽

Yanren Hou ◽

Xiaoxia Wang

Keyword(s):

Asymptotic Behavior ◽

Measure Of Noncompactness ◽

Dirichlet Boundary ◽

Stokes Equations ◽

Fractal Dimensions ◽

Dirichlet Boundary Conditions ◽

Navier Stokes ◽

Bounded Domains ◽

Pullback Attractors ◽

Navier Stokes Equations

AbstractThe pullback asymptotic behavior of the solutions for 2D Nonau-tonomousG-Navier-Stokes equations is studied, and the existence of itsL2-pullback attractors on some bounded domains with Dirichlet boundary conditions is investigated by using the measure of noncompactness. Then the estimation of the fractal dimensions for the 2DG-Navier-Stokes equations is given.

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Existence and Regularity Results for Anisotropic Elliptic Problems

Advanced Nonlinear Studies ◽

10.1515/ans-2009-0207 ◽

2009 ◽

Vol 9 (2) ◽

Cited By ~ 4

Author(s):

Agnese Di Castro

Keyword(s):

Boundary Conditions ◽

Dirichlet Boundary ◽

Elliptic Problems ◽

Dirichlet Boundary Conditions ◽

Bounded Domains ◽

Existence And Regularity Results ◽

Regularity Results ◽

Homogeneous Dirichlet Boundary Conditions

AbstractWe study existence and regularity of the solutions for some anisotropic elliptic problems with homogeneous Dirichlet boundary conditions in bounded domains.

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ON THE EXISTENCE AND UNIQUENESS OF SOLUTIONS TO 2D G-BÉNARD PROBLEM IN UNBOUNDED DOMAINS

Journal of Science Natural Science ◽

10.18173/2354-1059.2020-0025 ◽

2020 ◽

Vol 65 (6) ◽

pp. 23-30

Author(s):

Thinh Tran Quang ◽

Thuy Le Thi

Keyword(s):

Existence And Uniqueness ◽

Dirichlet Boundary ◽

Stokes Equations ◽

Dirichlet Boundary Conditions ◽

Navier Stokes ◽

Uniqueness Of Solutions ◽

Navier Stokes Equations ◽

Bénard Problem ◽

Benard Problem ◽

Homogeneous Dirichlet Boundary Conditions

We consider the 2D g-Bénard problem in domains satisfying the Poincaré inequality with homogeneous Dirichlet boundary conditions. We prove the existence and uniqueness of global weak solutions. The obtained results particularly extend previous results for 2D g-Navier-Stokes equations and 2D Bénard problem.

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Long-term behaviour in a chemotaxis-fluid system with logistic source

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s021820251640008x ◽

2016 ◽

Vol 26 (11) ◽

pp. 2071-2109 ◽

Cited By ~ 69

Author(s):

Johannes Lankeit

Keyword(s):

Boundary Conditions ◽

Dirichlet Boundary ◽

Neumann Boundary ◽

Dirichlet Boundary Conditions ◽

Navier Stokes ◽

Logistic Source ◽

State Formula ◽

Bounded Smooth ◽

Homogeneous Dirichlet Boundary Conditions

We consider the coupled chemotaxis Navier–Stokes model with logistic source terms: [Formula: see text] [Formula: see text] [Formula: see text] in a bounded, smooth domain [Formula: see text] under homogeneous Neumann boundary conditions for [Formula: see text] and [Formula: see text] and homogeneous Dirichlet boundary conditions for [Formula: see text] and with given functions [Formula: see text] satisfying certain decay conditions and [Formula: see text] for some [Formula: see text]. We construct weak solutions and prove that after some waiting time they become smooth and finally converge to the semi-trivial steady state [Formula: see text].

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On a Lp-estimate for the linearized compressible Navier–Stokes equations with the Dirichlet boundary conditions

Journal of Differential Equations ◽

10.1016/s0022-0396(02)00017-7 ◽

2002 ◽

Vol 186 (2) ◽

pp. 377-393 ◽

Cited By ~ 18

Author(s):

Piotr Bogusław Mucha ◽

Wojciech M. Zajączkowski

Keyword(s):

Boundary Conditions ◽

Dirichlet Boundary ◽

Stokes Equations ◽

Dirichlet Boundary Conditions ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Lp Estimate

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On the global regularity for singular p-systems under non-homogeneous Dirichlet boundary conditions

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2012.08.058 ◽

2013 ◽

Vol 398 (2) ◽

pp. 527-533 ◽

Cited By ~ 2

Author(s):

H. Beirão da Veiga

Keyword(s):

Boundary Conditions ◽

Dirichlet Boundary ◽

Global Regularity ◽

Dirichlet Boundary Conditions ◽

Homogeneous Dirichlet Boundary Conditions

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Convergence of the Finite-Difference Method for the 1—d Wave Equation with Homogeneous Dirichlet Boundary Conditions

Numerical Approximation of Exact Controls for Waves - SpringerBriefs in Mathematics ◽

10.1007/978-1-4614-5808-1_3 ◽

2013 ◽

pp. 59-78

Author(s):

Sylvain Ervedoza ◽

Enrique Zuazua

Keyword(s):

Wave Equation ◽

Finite Difference ◽

Finite Difference Method ◽

Boundary Conditions ◽

Difference Method ◽

Dirichlet Boundary ◽

Dirichlet Boundary Conditions ◽

The Finite Difference Method ◽

Homogeneous Dirichlet Boundary Conditions ◽

D Wave

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Exact solutions for restricted incompressible Navier–Stokes equations with Dirichlet boundary conditions

Journal of Physics Communications ◽

10.1088/2399-6528/ab3837 ◽

2019 ◽

Vol 3 (8) ◽

pp. 085008

Author(s):

Manuel García-Casado

Keyword(s):

Boundary Conditions ◽

Exact Solutions ◽

Dirichlet Boundary ◽

Stokes Equations ◽

Dirichlet Boundary Conditions ◽

Navier Stokes ◽

Navier Stokes Equations

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Global exponential stability and existence of periodic solutions for delayed reaction-diffusion BAM neural networks with Dirichlet boundary conditions

Boundary Value Problems ◽

10.1186/1687-2770-2013-105 ◽

2013 ◽

Vol 2013 (1) ◽

Cited By ~ 3

Author(s):

Weiyuan Zhang ◽

Junmin Li ◽

Minglai Chen

Keyword(s):

Neural Networks ◽

Boundary Conditions ◽

Exponential Stability ◽

Global Exponential Stability ◽

Dirichlet Boundary ◽

Reaction Diffusion ◽

Dirichlet Boundary Conditions ◽

Bam Neural Networks ◽

Delayed Reaction ◽

Existence Of Periodic Solutions

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On a 2D stochastic Euler equation of transport type: Existence and geometric formulation

Stochastics and Dynamics ◽

10.1142/s0219493714500129 ◽

2014 ◽

Vol 15 (01) ◽

pp. 1450012 ◽

Cited By ~ 3

Author(s):

Ana Bela Cruzeiro ◽

Iván Torrecilla

Keyword(s):

Boundary Conditions ◽

Euler Equation ◽

Multiplicative Noise ◽

Dirichlet Boundary ◽

Periodic Boundary Conditions ◽

Dirichlet Boundary Conditions ◽

Navier Stokes ◽

Navier Stokes Equation ◽

Geometric Formulation ◽

Transport Type

We prove weak existence of Euler equation (or Navier–Stokes equation) perturbed by a multiplicative noise on bounded domains of ℝ2 with Dirichlet boundary conditions and with periodic boundary conditions. Solutions are H1 regular. The equations are of transport type.

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