Global stability of large solutions for the Navier–Stokes equations with Navier boundary conditions

Benvenutti, Maicon J.; Ferreira, Lucas C. F.

doi:10.1016/j.nonrwa.2018.03.003

Nonlinear Analysis: Real World Applications

2018

DOI: 10.1016/j.nonrwa.2018.03.003

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Global stability of large solutions for the Navier–Stokes equations with Navier boundary conditions

Maicon J. Benvenutti

Lucas C. F. Ferreira

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“…The Navier-Stokes equations which considered Navier type boundary conditions were comprehensively studied in the references (see, e.g. [4,5,12,23]). Some development concerning the Boussinesq equations with Navier boundary conditions, we refer the readers to [22,32].…”

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confidence: 99%

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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mentioning

confidence: 99%

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

Sun¹,

Jiang²,

Liu³

2025

MFC

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

Wang

2021

Arch. Math.

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Global existence and large time behavior of strong solutions for 3D nonhomogeneous heat conducting Navier–Stokes equations

Zhong

2020

Journal of Mathematical Physics

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We are concerned with an initial boundary value problem of nonhomogeneous heat conducting Navier–Stokes equations on a bounded simply connected smooth domain Ω⊆R3, with the Navier-slip boundary condition for velocity and Neumann boundary condition for temperature. We prove that there exists a unique global strong solution, provided that ‖ρ0u0‖L22‖curlu0‖L22 is suitably small. Moreover, we also obtain the large time decay rates of the solution. Our result improves previous works on this topic.

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Global stability of large solutions for the Navier–Stokes equations with Navier boundary conditions

Cited by 3 publications

References 26 publications

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

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

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

Global existence and large time behavior of strong solutions for 3D nonhomogeneous heat conducting Navier–Stokes equations

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