Pullback attractors for 2D Navier–Stokes equations on time-varying domains

Song, Xiaoya; Sun, Chunyou; Yang, Lu

doi:10.1016/j.nonrwa.2018.07.013

Cited by 11 publications

(9 citation statements)

References 20 publications

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“…(18) at k = ∞. Indeed, by the weak formulation (20), the expansion v k * satisfies that, for each w ∈…”

Section: Weak Equi-continuitymentioning

confidence: 99%

“…Such an expanding-domain problem is contrary to the thin-domain problem, the latter was extensively investigated in the literature (see [14,15]) and time-varying domains problem [20]. However, the same difficulty arises from the fact that both A k and A ∞ lie in different phase spaces, compared with the same phase space in time-dependent stability of a pullback attractor [6,7,12].…”

Section: Introductionmentioning

confidence: 99%

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Large-domain stability of random attractors for stochastic g-Navier–Stokes equations with additive noise

She

2020

J Inequal Appl

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This paper concerns the long term behavior of the stochastic two-dimensional g-Navier-Stokes equations with additive noise defined on a sequence of expanding domains, where the ultimate domain is unbounded and of Poincaré type. We prove that the weak continuity is uniform with respect to all expanding cocycles, which yields the equi-asymptotic compactness by using an energy equation method. Finally, we show the existence of a random attractor for the equation on each domain and the upper semi-continuity of random attractors as the bounded domain is expanded to the unbounded ultimate domain.

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“…(18) at k = ∞. Indeed, by the weak formulation (20), the expansion v k * satisfies that, for each w ∈…”

Section: Weak Equi-continuitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Large-domain stability of random attractors for stochastic g-Navier–Stokes equations with additive noise

She

2020

J Inequal Appl

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“…It is worth pointing out that such thin domains problems for random dynamical systems is contrary to the expanding domains problems [26,33] and different from time-varying domains [20,44]. In particular, the upper semi-continuity on thin domains is also different from time-variable problem [13,21,35,34,46], delay problem [22,23,43,47,48] and Wong-Zakai approximations [16,15,37,49].…”

mentioning

confidence: 95%

Regular dynamics for stochastic Fitzhugh-Nagumo systems with additive noise on thin domains

Li¹,

Xu²

2021

DCDS-B

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This paper is devoted to bi-spatial random attractors of the stochastic Fitzhugh-Nagumo equations with additive noise on thin domains when the terminate space is the Sobolev space. We first established the existence of random attractor on regular space and then show that the upper semicontinuity of these attractors under the Sobolev norm when a family of (n + 1)dimensional thin domains degenerates onto an n-dimensional domain.

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“…Notably, problems on thin domains for random dynamical systems are contrary to those in expanding domains 30 and different from those in time-varying domains. 31,32 Moreover, the upper semi-continuity of thin domains is also different from that of the time variable [33][34][35][36][37] and delay. [38][39][40][41] This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Dynamics for stochastic Fitzhugh–Nagumo systems with general multiplicative noise on thin domains

2020

Math Methods in App Sciences

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This paper is devoted to studying the dynamics for stochastic Fitzhugh–Nagumo equations with general multiplicative noise on thin domains, where the noise is described by a general stochastic process instead of the usual Wiener process. The measurability of the solution operator is proved, which yields to the measurability of the random attractor. We then show the existence and upper semi‐continuity of these attractors when a family of (n + 1)‐dimensional thin domains degenerates onto an n‐dimensional domain under the topology of p‐times Lebesgue space.

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Pullback attractors for 2D Navier–Stokes equations on time-varying domains

Cited by 11 publications

References 20 publications

Large-domain stability of random attractors for stochastic g-Navier–Stokes equations with additive noise

Large-domain stability of random attractors for stochastic g-Navier–Stokes equations with additive noise

Regular dynamics for stochastic Fitzhugh-Nagumo systems with additive noise on thin domains

Dynamics for stochastic Fitzhugh–Nagumo systems with general multiplicative noise on thin domains

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