scholarly journals The existence and exponential behavior of solutions to time fractional stochastic delay evolution inclusions with nonlinear multiplicative noise and fractional noise

2020 ◽  
Vol 25 (7) ◽  
pp. 2665-2697
Author(s):  
Yajing Li ◽  
◽  
Yejuan Wang ◽  
Keyword(s):  
Multiplicative Noise ◽  
Evolution Inclusions ◽  
Exponential Behavior ◽  
Stochastic Delay ◽  
Fractional Noise

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].

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