On the global stability of large solutions for the Boussinesq equations with Navier boundary conditions

Wang, Weinan

doi:10.1007/s00013-020-01557-x

Cited by 4 publications

(2 citation statements)

References 22 publications

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“…For other global well-posedness results on the Boussinesq equations, cf. [HK1,W1,W2,WY2]. The 3D Boussinesq system possesses a natural scaling, i.e., for λ > 0, u λ (x, t) = λu(λx, λ 2 t), ρ λ (x, t) = λ 3 ρ(λx, λ 2 t)…”

Section: Introductionmentioning

confidence: 99%

Norm inflation for the Boussinesq system

Li,

Wang

2019

Preprint

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We prove the norm inflation phenomena for the Boussinesq system on T 3 . For arbitrarily small initial data (u0, ρ0) in the negative-order Besov spaces Ḃ−1 ∞,∞ × Ḃ−1 ∞,∞ , the solution can become arbitrarily large in a short time. Such largeness can be detected in ρ in Besov spaces of any negative order: Ḃ−s ∞,∞ for any s > 0. Notice that our initial data space is scaling critical for u and is scaling subcritical for ρ.

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Section: Introductionmentioning

confidence: 99%

Norm inflation for the Boussinesq system

Li,

Wang

2019

Preprint

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“…[4,5,12,23]). Some development concerning the Boussinesq equations with Navier boundary conditions, we refer the readers to [22,32]. For more research results to the Boussinesq equations with other type boundary conditions, see [2,8].…”

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Study on the well-posedness of stochastic Boussinesq equations with Navier boundary conditions

Sun¹,

Jiang²,

Liu³

2025

MFC

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Due to the Navier boundary conditions (first introduced in [28]) which allow the fluid to slip along the boundary are more consistent with the actual physical background, we consider stochastic Boussinesq equations in a 2D-bounded domain with Navier type boundary conditions in this paper. First, we obtain a priori estimates of the weak solutions of stochastic Boussinesq equations in L 2 and L 4 via Itô's formula and the BurkHölder-Davis-Gundy's inequality. Then, we establish the existence and uniqueness of the weak solutions which base on a priori estimates and monotonicity arguments. Different from the periodic conditions and the Dirichlet conditions, the Navier boundary conditions generate boundary terms on velocity by integration by parts, and we attempt to over come the difficulties cased by boundary terms. Based on the theory of the existence of equations, we can gain a better understanding of the essence and mathematical structure, thereby guiding the strategy and technique selection for numerical solving.

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On Asymptotic Stability of the 3D Boussinesq Equations with a Velocity Damping Term

Li-hua

2022

J. Math. Fluid Mech.

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On the global stability of large solutions for the Boussinesq equations with Navier boundary conditions

Cited by 4 publications

References 22 publications

Norm inflation for the Boussinesq system

Norm inflation for the Boussinesq system

Study on the well-posedness of stochastic Boussinesq equations with Navier boundary conditions

On Asymptotic Stability of the 3D Boussinesq Equations with a Velocity Damping Term

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