scholarly journals The exponential behavior of a stochastic Cahn-Hilliard-Navier-Stokes model with multiplicative noise

2019 ◽  
Vol 18 (6) ◽  
pp. 2961-2982
Author(s):  
T. Tachim Medjo ◽  
Keyword(s):  
Multiplicative Noise ◽  
Navier Stokes ◽  
Exponential Behavior

The exponential behavior and stabilizability of the stochastic 3D Navier–Stokes equations with damping

2019 ◽  
Vol 31 (07) ◽  
pp. 1950023 ◽  
Author(s):  
Hui Liu ◽  
Lin Lin ◽  
Chengfeng Sun ◽  
Qingkun Xiao
Keyword(s):  
Weak Solutions ◽  
Multiplicative Noise ◽  
Stokes Equations ◽  
Stationary Solutions ◽  
Navier Stokes ◽  
Exponential Behavior ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
The Mean ◽  
The Stability

The stochastic 3D Navier–Stokes equation with damping driven by a multiplicative noise is considered in this paper. The stability of weak solutions to the stochastic 3D Navier–Stokes equations with damping is proved for any [Formula: see text] with any [Formula: see text] and [Formula: see text] as [Formula: see text]. The weak solutions converge exponentially in the mean square and almost surely exponentially to the stationary solutions are proved for any [Formula: see text] with any [Formula: see text] and [Formula: see text] as [Formula: see text]. The stabilization of these equations is obtained for any [Formula: see text] with any [Formula: see text] and [Formula: see text] as [Formula: see text].

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

2014 ◽  
Vol 15 (01) ◽  
pp. 1450012 ◽  
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.

Navier-Stokes equations with multiplicative noise

Nonlinearity ◽  
1993 ◽  
Vol 6 (1) ◽  
pp. 71-78 ◽  
Author(s):  
M Capinski ◽  
N J Cutland
Keyword(s):  
Multiplicative Noise ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

ATTRACTORS AND NEO-ATTRACTORS FOR 3D STOCHASTIC NAVIER–STOKES EQUATIONS

2005 ◽  
Vol 05 (04) ◽  
pp. 487-533 ◽  
Author(s):  
NIGEL J. CUTLAND ◽  
H. JEROME KEISLER
Keyword(s):  
Global Attractor ◽  
Ad Hoc ◽  
Multiplicative Noise ◽  
Stokes Equations ◽  
Nonstandard Analysis ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Loeb Space

In [14] nonstandard analysis was used to construct a (standard) global attractor for the 3D stochastic Navier–Stokes equations with general multiplicative noise, living on a Loeb space, using Sell's approach [26]. The attractor had somewhat ad hoc attracting and compactness properties. We strengthen this result by showing that the attractor has stronger properties making it a neo-attractor — a notion introduced here that arises naturally from the Keisler–Fajardo theory of neometric spaces [18]. To set this result in context we first survey the use of Loeb space and nonstandard techniques in the study of attractors, with special emphasis on results obtained for the Navier–Stokes equations both deterministic and stochastic, showing that such methods are well-suited to this enterprise.

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