The initial value problem for the non-homogeneous Navier—Stokes equations with general slip boundary condition

2000 ◽  
Vol 130 (4) ◽  
pp. 827-835 ◽  
Author(s):  
S. Itoh ◽  
A. Tani
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Solid Boundary ◽  
Dimensional Problem ◽  
Navier Stokes Equations ◽  
Slip Boundary

The initial-boundary value problem for the non-homogeneous Navier-Stokes equations including the slipping on the solid boundary is considered. The unique solvability is established locally in time for the three-dimensional problem and globally in time for the two-dimensional problem without so-called smallness restrictions.

scholarly journals Axisymmetric flows in the exterior of a cylinder

2019 ◽  
Vol 150 (4) ◽  
pp. 1671-1698 ◽  
Author(s):  
K. Abe ◽  
G. Seregin
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Initial Boundary Value

AbstractWe study an initial-boundary value problem of the three-dimensional Navier-Stokes equations in the exterior of a cylinder $\Pi =\{x=(x_{h}, x_3)\ \vert \vert x_{h} \vert \gt 1\}$, subject to the slip boundary condition. We construct unique global solutions for axisymmetric initial data $u_0\in L^{3}\cap L^{2}(\Pi )$ satisfying the decay condition of the swirl component $ru^{\theta }_{0}\in L^{\infty }(\Pi )$.

Attractors for the modifications of the three-dimensional Navier-Stokes equations

1994 ◽  
Vol 346 (1679) ◽  
pp. 173-190 ◽  
Keyword(s):  
Viscous Fluid ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Fluid Flows ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Initial Boundary Value ◽  
Dimensional Domain

The modifications of the three-dimensional Navier-Stokes equations, which I suggested earlier for the description of viscous fluid flows with large gradients of velocities, are considered. It is proved that the first initial-boundary value problem for these equations in any bounded three-dimensional domain has a compact minimal global B-attractor. Some properties of the attractor are established.

scholarly journals Global Existence of the Cylindrically Symmetric Strong Solution to Compressible Navier-Stokes Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Jian Liu ◽  
Ruxu Lian
Keyword(s):  
Strong Solution ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Cylindrically Symmetric ◽  
Initial Boundary Value ◽  
Dependent Viscosity

This paper is concerned with the initial boundary value problem for the three-dimensional Navier-Stokes equations with density-dependent viscosity. The cylindrically symmetric strong solution is shown to exist globally in time and tend to the equilibrium state exponentially as time grows up.

scholarly journals Involving the Navier–Stokes equations in the derivation of boundary conditions for the lattice Boltzmann method

2011 ◽  
Vol 369 (1944) ◽  
pp. 2184-2192 ◽  
Author(s):  
Joris C. G. Verschaeve
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Grid Spacing ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Boltzmann Method

By means of the continuity equation of the incompressible Navier–Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.

GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF THE COMPRESSIBLE NAVIER–STOKES EQUATIONS FOR A 1D ISOTHERMAL VISCOUS GAS

2008 ◽  
Vol 18 (08) ◽  
pp. 1383-1408 ◽  
Author(s):  
YUMING QIN ◽  
YANLI ZHAO
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Stokes Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Navier Stokes ◽  
Asymptotic Behavior Of Solutions ◽  
Navier Stokes Equations ◽  
Viscous Gas ◽  
Initial Boundary Value

In this paper, we prove the global existence and asymptotic behavior of solutions in Hi(i = 1, 2) to an initial boundary value problem of a 1D isentropic, isothermal and the compressible viscous gas with an non-autonomous external force in a bounded region.

scholarly journals Regularity Criteria for Navier-Stokes Equations with Slip Boundary Conditions on Non-flat Boundaries via Two Velocity Components

2019 ◽  
Vol 9 (1) ◽  
pp. 633-643
Author(s):  
Hugo Beirão da Veiga ◽  
Jiaqi Yang
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Regularity Criteria ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Whole Space ◽  
Space Case

Abstract H.-O. Bae and H.J. Choe, in a 1997 paper, established a regularity criteria for the incompressible Navier-Stokes equations in the whole space ℝ3 based on two velocity components. Recently, one of the present authors extended this result to the half-space case $\begin{array}{} \displaystyle \mathbb{R}^3_+ \end{array}$. Further, this author in collaboration with J. Bemelmans and J. Brand extended the result to cylindrical domains under physical slip boundary conditions. In this note we obtain a similar result in the case of smooth arbitrary boundaries, but under a distinct, apparently very similar, slip boundary condition. They coincide just on flat portions of the boundary. Otherwise, a reciprocal reduction between the two results looks not obvious, as shown in the last section below.

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