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Artículo
Morse decomposition for gradient-like multi-valued autonomous and nonautonomous dynamical systems
(American Institute of Mathematical Sciences (AIMS), 2020-08)
In this paper, we first prove that the property of being a gradientlike general dynamical system and the existence of a Morse decomposition are equivalent. Next, the stability of gradient-like general dynamical systems ...
Artículo
Regularity of global attractors and exponential attractors for 2D quasi-geostrophic equations with fractional dissipation
(AIMS, 2021-01)
In this paper we investigate the regularity of global attractors and of exponential attractors for two dimensional quasi-geostrophic equations with fractional dissipation in H2α+s (T 2 ) with α > 1 2 and s > 1. We ...
Artículo
Exponential behavior and upper noise excitation index of solutions to evolution equations with unbounded delay and tempered fractional Brownian motions
(Springer, 2021-01-02)
In this paper, we investigate stochastic evolution equations with unbounded delay in fractional power spaces perturbed by a tempered fractional Brownian motion Bσ,λQ(t)BQσ,λ(t) with −1/2<σ<0−1/2<σ<0 and λ>0λ>0. We first ...
Artículo
The continuity, regularity and polynomial stability of mild solutions for stochastic 2D-Stokes equations with unbounded delay driven by tempered fractional Gaussian noise
(World scientific, 2021-09)
We consider stochastic 2D-Stokes equations with unbounded delay in fractional power spaces and moments of order p ≥ 2 driven by a tempered fractional Brownian motion (TFBM) Bσ,λ(t) with −1/2 < σ < 0 and λ > 0. First, the ...
Artículo
Exponential behavior and upper noise excitation index of solutions to evolution equations with unbounded delay and tempered fractional Brownian motions
(Springer, 2021-01-02)
In this paper, we investigate stochastic evolution equations with unbounded delay in fractional power spaces perturbed by a tempered fractional Brownian motion Bσ,λQ(t) with −1/2<σ<0 and λ>0. We first introduce a technical ...
Artículo
Stability of fractionally dissipative 2D quasi-geostrophic equation with infinite delay
(Springer, 2020-08-18)
In this paper, fractionally dissipative 2D quasi-geostrophic equations with an external force containing infinite delay is considered in the space Hs with s ≥ 2 − 2α and α ∈ ( 1 2 , 1). First, we investigate the existence ...