NAVIER–STOKES SYSTEM ON THE FLAT CYLINDER AND UNIT SQUARE WITH SLIP BOUNDARY CONDITIONS

2010 ◽  
Vol 12 (02) ◽  
pp. 325-349 ◽  
Author(s):  
EFIM DINABURG ◽  
DONG LI ◽  
YAKOV G. SINAI
Keyword(s):  
Boundary Conditions ◽  
Initial Velocity ◽  
Stokes System ◽  
Navier Stokes ◽  
Decay Estimates ◽  
Two Dimensional ◽  
Slip Boundary Conditions ◽  
Unit Square ◽  
Slip Boundary

We study the decay of Fourier modes of solutions to the two-dimensional Navier–Stokes System on a flat cylinder and the unit square with slip boundary conditions. Under some suitable assumptions on the initial velocity, we obtain quantitative decay estimates of the Fourier modes.

scholarly journals Asymptotic analysis of an optimal control problem for a viscous incompressible fluid with Navier slip boundary conditions

2021 ◽  
pp. 1-21
Author(s):  
Claudia Gariboldi ◽  
Takéo Takahashi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Conditions ◽  
Control Problem ◽  
Stokes System ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Slip ◽  
Slip Boundary ◽  
Navier Slip Boundary Conditions

We consider an optimal control problem for the Navier–Stokes system with Navier slip boundary conditions. We denote by α the friction coefficient and we analyze the asymptotic behavior of such a problem as α → ∞. More precisely, we prove that if we take an optimal control for each α, then there exists a sequence of optimal controls converging to an optimal control of the same optimal control problem for the Navier–Stokes system with the Dirichlet boundary condition. We also show the convergence of the corresponding direct and adjoint states.

scholarly journals Correlation between No-Slip and Slip Boundary Conditions Associated with A Two-Dimensional Navier-Stokes Flows in a Plane Diffuser

2021 ◽  
Vol 65 (1) ◽  
pp. 1-23
Author(s):  
Ranis Ibragimov ◽  
◽  
Vesselin Vatchev ◽  
Keyword(s):  
Boundary Conditions ◽  
Small Perturbation ◽  
Taylor Series Expansion ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Slip Boundary Conditions ◽  
Viscous Effects ◽  
Stokes Flows ◽  
Slip Boundary ◽  
Two Parameters

We examine the viscous effects of slip boundary conditions for the model describing two-dimensional Navier-Stokes flows in a plane diffuser. It is shown that the velocity profile is related to a half period shifted Weierstrass function with two parameters. This allows to approximate the explicit solution by a Taylor series expansion with two new micro- parameters, that can be measured in physical experiments. It is shown that the assumption for no-slip boundary conditions is stable in the sense that a small perturbation of the boundary values result in a small perturbation in the solutions.

scholarly journals On incompressible limits for the Navier-Stokes system on unbounded domains under slip boundary conditions

2010 ◽  
Vol 13 (4) ◽  
pp. 783-798 ◽  
Author(s):  
Donatella Donatelli ◽  
◽  
Eduard Feireisl ◽  
Antonín Novotný ◽  
◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Stokes System ◽  
Unbounded Domains ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Slip Boundary

scholarly journals Weak solutions to the barotropic Navier–Stokes system with slip boundary conditions in time dependent domains

2013 ◽  
Vol 254 (1) ◽  
pp. 125-140 ◽  
Author(s):  
Eduard Feireisl ◽  
Ondřej Kreml ◽  
Šárka Nečasová ◽  
Jiří Neustupa ◽  
Jan Stebel
Keyword(s):  
Boundary Conditions ◽  
Weak Solutions ◽  
Stokes System ◽  
Time Dependent ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Slip Boundary

scholarly journals Local existence of strong solutions and weak–strong uniqueness for the compressible Navier–Stokes system on moving domains

2019 ◽  
Vol 150 (5) ◽  
pp. 2255-2300 ◽  
Author(s):  
Ondřej Kreml ◽  
Šárka Nečasová ◽  
Tomasz Piasecki
Keyword(s):  
Boundary Conditions ◽  
Stokes System ◽  
Local Existence ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Strong Uniqueness ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Moving Domains ◽  
Open Question

AbstractWe consider the compressible Navier–Stokes system on time-dependent domains with prescribed motion of the boundary. For both the no-slip boundary conditions as well as slip boundary conditions we prove local-in-time existence of strong solutions. These results are obtained using a transformation of the problem to a fixed domain and an existence theorem for Navier–Stokes like systems with lower order terms and perturbed boundary conditions. We also show the weak–strong uniqueness principle for slip boundary conditions which remained so far open question.

scholarly journals Bifurcations in a quasi-two-dimensional Kolmogorov-like flow

2017 ◽  
Vol 828 ◽  
pp. 837-866 ◽  
Author(s):  
Jeffrey Tithof ◽  
Balachandra Suri ◽  
Ravi Kumar Pallantla ◽  
Roman O. Grigoriev ◽  
Michael F. Schatz
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Quantitative Agreement ◽  
Navier Stokes ◽  
Dielectric Fluid ◽  
Two Dimensional ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
2D Model

We present a combined experimental and theoretical study of the primary and secondary instabilities in a Kolmogorov-like flow. The experiment uses electromagnetic forcing with an approximately sinusoidal spatial profile to drive a quasi-two-dimensional (Q2D) shear flow in a thin layer of electrolyte suspended on a thin lubricating layer of a dielectric fluid. Theoretical analysis is based on a two-dimensional (2D) model (Suri et al., Phys. Fluids, vol. 26 (5), 2014, 053601), derived from first principles by depth-averaging the full three-dimensional Navier–Stokes equations. As the strength of the forcing is increased, the Q2D flow in the experiment undergoes a series of bifurcations, which is compared with results from direct numerical simulations of the 2D model. The effects of confinement and the forcing profile are studied by performing simulations that assume spatial periodicity and strictly sinusoidal forcing, as well as simulations with realistic no-slip boundary conditions and an experimentally validated forcing profile. We find that only the simulation subject to physical no-slip boundary conditions and a realistic forcing profile provides close, quantitative agreement with the experiment. Our analysis offers additional validation of the 2D model as well as a demonstration of the importance of properly modelling the forcing and boundary conditions.

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