uniqueness and asymptotic behavior of the stationary Navier-Stokes equations in a slab
Han Li, Jingwen Han
Abstract
In this paper, we investigate the uniqueness and asymptotic behavior of the stationary Navier-Stokes equations in a slab domain with no-slip boundary conditions. Specifically, under the given external force and the small Poiseuille flow assumptions, we prove that there is an H1 solution, and obtain the pointwise decay around the Poiseuille flow at far field. Furthermore, if the force is small, the solution is shown to be unique. The key point of the proof is the estimate of the Dirichlet integral of the solutions in the truncated domains and the Stokes regularity estimates.
Create a lesson
Related papers
Learning Lyapunov Operators for Nonlinear Systems
Amartya Mukherjee, Maxwell Fitzsimmons, David C. Del Rey Fernández et al.
Existence of Admissible Subsolutions to the Dirichlet Problem for Symmetric Augmented k-Hessian Type Equations in Bounded Domains
Quang Hong Dinh, Bang Van Tran, Ngoan Tien Ha et al.
The Regularity datum on time-varying graph domains and Dirichlet--Regularity duality
Martin Dindoš
Existence of flat blowups at boundary points of anisotropic minimizing hypercurrents
Michael Novack, Reinaldo Resende
Isolated singularities of the capillary equation with negative gravity
Bin Deng, Jiahuan Li, Yilu Liu et al.
Local behavior for solutions to inhomogeneous singular parabolic p-Laplace equations
Xia Hao, Yan Li, Zhiwen Zhao