scholarly journals Asymptotic stability of 3D functional Brinkman-Forchheimer equation

2021 ◽  
Author(s):  
Xinguang Yang ◽  
Yong Yang ◽  
Wenjing Liu ◽  
Junzhao Zhang
Keyword(s):  
Asymptotic Stability ◽  
Flow Model ◽  
Global Solutions ◽  
Strong Solutions ◽  
State Equation ◽  
Forchheimer Equation ◽  
Steady State Equation ◽  
External Forces ◽  
Equation With Delay ◽  
Forchheimer Flow

This paper is concerned with the asymptotic stability of global weak and strong solutions for a 3D incompressible functional Brinkman-Forchheimer equation with delay. Under some appropriate assumptions on the external forces especially the averaged state, the well-posedness of 3D functional Brinkman-Forchheimer flow model and its steady state equation have been obtained rstly, then the asymptotic stability of global solutions also derived via the convergence of trajectories for the corresponding systems.

scholarly journals Strong Solutions of the Incompressible Navier–Stokes–Voigt Model

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 181
Author(s):  
Evgenii S. Baranovskii
Keyword(s):  
Three Dimensional ◽  
Strong Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Navier Stokes ◽  
Evolutionary Equation ◽  
Long Time ◽  
Special Basis ◽  
External Forces ◽  
Initial Boundary Value

This paper deals with an initial-boundary value problem for the Navier–Stokes–Voigt equations describing unsteady flows of an incompressible non-Newtonian fluid. We give the strong formulation of this problem as a nonlinear evolutionary equation in Sobolev spaces. Using the Faedo–Galerkin method with a special basis of eigenfunctions of the Stokes operator, we construct a global-in-time strong solution, which is unique in both two-dimensional and three-dimensional domains. We also study the long-time asymptotic behavior of the velocity field under the assumption that the external forces field is conservative.

scholarly journals Strong Uniform Attractors for Nonautonomous Suspension Bridge-Type Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
Xuan Wang ◽  
Qiaozhen Ma
Keyword(s):  
Hilbert Space ◽  
Dynamical Behavior ◽  
Type Equation ◽  
Strong Solutions ◽  
Suspension Bridge ◽  
Bridge Type ◽  
Uniform Attractors ◽  
External Forces ◽  
Higher Regularity

We discuss long-term dynamical behavior of the solutions for the nonautonomous suspension bridge-type equation in the strong Hilbert spaceD(A)×H2(Ω)∩H01(Ω), where the nonlinearityg(u,t)is translation compact and the time-dependent external forcesh(x,t)only satisfy condition (C*) instead of translation compact. The existence of strong solutions and strong uniform attractors is investigated using a new process scheme. Since the solutions of the nonautonomous suspension bridge-type equation have no higher regularity and the process associated with the solutions is not continuous in the strong Hilbert space, the results are new and appear to be optimal.

A determination of the effective viscosity for the Brinkman–Forchheimer flow model

1994 ◽  
Vol 258 ◽  
pp. 355-370 ◽  
Author(s):  
R. C. Givler ◽  
S. A. Altobelli
Keyword(s):  
Effective Viscosity ◽  
Average Velocity ◽  
Flow Model ◽  
High Porosity ◽  
Rigid Foam ◽  
Nmr Techniques ◽  
Flow Through ◽  
Forchheimer Flow ◽  
Average Velocity Profile

The effective viscosity μe for the Brinkman–Forchheimer flow (BFF) model has been determined experimentally for steady flow through a wall-bounded porous medium. Nuclear magnetic resonance (NMR) techniques were used to measure non-invasively the ensemble-average velocity profile of water flowing through a tube filled with an open-cell rigid foam of high porosity (ϕ = 0.972). By comparing these data with the BFF model, for which all remaining parameters were measured independently, it was determined that μe = (7.5+3.4−2.4)μf, where μf was the viscosity of the fluid. The Reynolds number, based upon the square root of the permeability, was 17.

scholarly journals Magneto-micropolar fluid motion: global existence of strong solutions

1999 ◽  
Vol 4 (2) ◽  
pp. 109-125 ◽  
Author(s):  
Elva E. Ortega-Torres ◽  
Marko A. Rojas-Medar
Keyword(s):  
Global Existence ◽  
Galerkin Method ◽  
Error Bounds ◽  
Micropolar Fluid ◽  
Fluid Motion ◽  
Strong Solutions ◽  
Approximate Solutions ◽  
Time Estimates ◽  
Spectral Galerkin Method ◽  
External Forces

By using the spectral Galerkin method, we prove a result on global existence in time of strong solutions for the motion of magneto-micropolar fluid without assuming that the external forces decay with time. We also derive uniform in time estimates of the solution that are useful for obtaining error bounds for the approximate solutions.

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