Dynamics of the 2D Navier-Stokes equations with sublinear operators in Lipschitz-like domains

Yang, Xin-Guang; Wang, Rong-Nian; Yan, Xuehua; Miranville, Alain

doi:10.3934/dcds.2020408

Cited by 6 publications

(7 citation statements)

References 37 publications

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“…The Navier-Stokes equations with delay have also become interesting topics in the recent two decades, which are important dominant physical models for fluid mechanics, such as the wind tunnel model. The research on the well-posedness and dynamics of Navier-Stokes equations with delay can be seen in [4][5][6][7][8][9][10][11][12] and the literature therein. For the Navier-Stokes system with time-varying delay, the tempered pullback dynamics are obtained by energy equation approach to achieve compactness, such as in Caraballo and Real [5][6][7], García-Luengo and Marín-Rubio [9] and Yang, Wang, Yan and Miranville [12].…”

Section: Introductionmentioning

confidence: 99%

“…The research on the well-posedness and dynamics of Navier-Stokes equations with delay can be seen in [4][5][6][7][8][9][10][11][12] and the literature therein. For the Navier-Stokes system with time-varying delay, the tempered pullback dynamics are obtained by energy equation approach to achieve compactness, such as in Caraballo and Real [5][6][7], García-Luengo and Marín-Rubio [9] and Yang, Wang, Yan and Miranville [12]. Recently, Su, Yang, Miranville and Yang [11] considered (2) and derived the well-posedness, regularity, pullback dynamics and robustness.…”

Section: Introductionmentioning

confidence: 99%

“…Since there are two delays contained in (2), the energy estimates cannot be obtained by using the technique as in [15,17] to achieve the desired estimate for using differential Gronwall inequalities, which is the main difficulty here. By introducing a new retard Gronwall inequality in [13], and using the iteration technique, one sufficient condition (12) on generalized Grashof number guarantees our asymptotic stability; see Theorem 5 in Section 2.4. (II) The results in this presented paper are a further research of [15], which is a special case of (2).…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic Stability for the 2D Navier–Stokes Equations with Multidelays on Lipschitz Domain

Zhang

Yang

2022

Mathematics

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This paper is concerned with the asymptotic stability derived for the two-dimensional incompressible Navier–Stokes equations with multidelays on Lipschitz domain, which models the control theory of 2D fluid flow. By a new retarded Gronwall inequality and estimates of stream function for Stokes equations, the complete trajectories inside pullback attractors are asymptotically stable via the restriction on the generalized Grashof number of fluid flow. The results in this presented paper are some extension of the literature by Yang, Wang, Yan and Miranville in 2021, as well as also the preprint by Su, Yang, Miranville and Yang in 2022

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Asymptotic Stability for the 2D Navier–Stokes Equations with Multidelays on Lipschitz Domain

Zhang

Yang

2022

Mathematics

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“…The delay effect was first researched in the boundary controllers in engineering (see [44,45], and the references therein). Navier-Stokes equations with the delay terms have been studied initially in [4,5,6], they considered the existence, uniqueness, stationary solutions, exponential decay, existence of attractors, etc.…”

mentioning

confidence: 99%

“…which in particular will imply the relative compactness. In order to obtain this aim, due to the fact (44), we only need to show…”

mentioning

confidence: 99%

Dynamics for the 3D incompressible Navier-Stokes equations with double time delays and damping

Shi

Cui

et al. 2022

DCDS-B

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<p style='text-indent:20px;'>This paper is concerned with the tempered pullback attractors for 3D incompressible Navier-Stokes model with a double time-delays and a damping term. The delays are in the convective term and external force, which originate from the control in engineer and application. Based on the existence of weak and strong solutions for three dimensional hydrodynamical model with subcritical nonlinearity, we proved the existence of minimal family for pullback attractors with respect to tempered universes for the non-autonomous dynamical systems.</p>

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Dynamics and robustness for the 2D Navier–Stokes equations with multi-delays in Lipschitz-like domains

Yang

Miranville

et al. 2023

Asymptotic Analysis

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This paper is concerned with the dynamics of the two-dimensional Navier–Stokes equations with multi-delays in a Lipschitz-like domain, subject to inhomogeneous Dirichlet boundary conditions. The regularity of global solutions and of pullback attractors, based on tempered universes, is established, extending the results of Yang, Wang, Yan and Miranville (Discrete Contin. Dyn. Syst. 41 (2021) 3343–3366). Furthermore, the robustness of pullback attractors when the delays, considered as small perturbations, disappear is also derived. The key technique in the proofs is the application of a retarded Gronwall inequality and a variable index for the tempered pullback dynamics, allowing to obtain uniform estimates and the compactness of the process.

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Dynamics of the 2D Navier-Stokes equations with sublinear operators in Lipschitz-like domains

Cited by 6 publications

References 37 publications

Asymptotic Stability for the 2D Navier–Stokes Equations with Multidelays on Lipschitz Domain

Asymptotic Stability for the 2D Navier–Stokes Equations with Multidelays on Lipschitz Domain

Dynamics for the 3D incompressible Navier-Stokes equations with double time delays and damping

Dynamics and robustness for the 2D Navier–Stokes equations with multi-delays in Lipschitz-like domains

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