WEIGHTED Lq-SOLVABILITY OF THE STEADY STOKES SYSTEM IN DOMAINS WITH NONCOMPACT BOUNDARIES

1996 ◽  
Vol 06 (01) ◽  
pp. 97-136 ◽  
Author(s):  
K. PILECKAS
Keyword(s):  
Incompressible Fluid ◽  
Coordinate System ◽  
Lipschitz Condition ◽  
Sobolev Spaces ◽  
Stokes System ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Weighted Sobolev Spaces

The stationary Stokes equations of a viscous incompressible fluid are considered in domains Ω with m > 1 exits to infinity, which have in some coordinate system the following form: [Formula: see text] where gi are functions satisfying the global Lipschitz condition and [Formula: see text] as xn→ ∞. The solvability of the Stokes system with prescribed fluxes is investigated in weighted Sobolev spaces, which are generated by different weighted L q norms.

CLASSICAL SOLVABILITY AND UNIFORM ESTIMATES FOR THE STEADY STOKES SYSTEM IN DOMAINS WITH NONCOMPACT BOUNDARIES

1996 ◽  
Vol 06 (02) ◽  
pp. 149-167 ◽  
Author(s):  
K. PILECKAS
Keyword(s):  
Incompressible Fluid ◽  
Coordinate System ◽  
Lipschitz Condition ◽  
Stokes System ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Uniform Estimates ◽  
Classical Solvability ◽  
Weighted Hölder Spaces ◽  
Pointwise Decay

The stationary Stokes equations of a viscous incompressible fluid are considered in domains Ω with m > 1 outlets to infinity, which have in some coordinate system the following form [Formula: see text] where gi are functions satisfying the global Lipschitz condition and g'i (xn) → 0 as xn → ∞. In this paper we prove the solvability of the Stokes system with prescribed fluxes in weighted Hölder spaces and we show the pointwise decay of the solutions.

scholarly journals SOLUTIONS OF THE DIVERGENCE AND ANALYSIS OF THE STOKES EQUATIONS IN PLANAR HÖLDER-α DOMAINS

2010 ◽  
Vol 20 (01) ◽  
pp. 95-120 ◽  
Author(s):  
RICARDO G. DURÁN ◽  
FERNANDO LÓPEZ GARCÍA
Keyword(s):  
Sobolev Spaces ◽  
Existence Of Solutions ◽  
Stokes Equations ◽  
Basic Result ◽  
Weighted Sobolev Spaces ◽  
Mean Value ◽  
Well Posedness ◽  
Existence Of A Solution ◽  
Simply Connected ◽  
Distance To The Boundary

If Ω ⊂ ℝn is a bounded domain, the existence of solutions [Formula: see text] of div u = f for f ∈ L2(Ω) with vanishing mean value, is a basic result in the analysis of the Stokes equations. In particular, it allows to show the existence of a solution [Formula: see text], where u is the velocity and p the pressure. It is known that the above-mentioned result holds when Ω is a Lipschitz domain and that it is not valid for arbitrary Hölder-α domains. In this paper we prove that if Ω is a planar simply connected Hölder-α domain, there exist solutions of div u = f in appropriate weighted Sobolev spaces, where the weights are powers of the distance to the boundary. Moreover, we show that the powers of the distance in the results obtained are optimal. For some particular domains with an external cusp, we apply our results to show the well-posedness of the Stokes equations in appropriate weighted Sobolev spaces obtaining as a consequence the existence of a solution [Formula: see text] for some r < 2 depending on the power of the cusp.

scholarly journals Stability Analysis of Symmetrical Rotors Partially Filled with a Viscous Incompressible Fluid

2001 ◽  
Vol 7 (5) ◽  
pp. 301-310 ◽  
Author(s):  
Zhu Changsheng
Keyword(s):  
Stability Analysis ◽  
Incompressible Fluid ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Damping Ratio ◽  
Navier Stokes ◽  
Fluid Viscosity ◽  
Navier Stokes Equations ◽  
Rotor Systems ◽  
The Stability

On the basis of the linearized fluid forces acting on the rotor obtained directly by using the two-dimensional Navier-Stokes equations, the stability of symmetrical rotors with a cylindrical chamber partially filled with a viscous incompressible fluid is investigated in this paper. The effects of the parameters of rotor system, such as external damping ratio, fluid fill ratio, Reynolds number and mass ratio, on the unstable regions are analyzed. It is shown that for the stability analysis of fluid filled rotor systems with external damping, the effect of the fluid viscosity on the stability should be considered. When the fluid viscosity is included, the adding external damping will make the system more stable and two unstable regions may exist even if rotors are isotropic in some casIs.

scholarly journals On the reconstruction of obstacles and of rigid bodies immersed in a viscous incompressible fluid

2017 ◽  
Vol 25 (1) ◽  
pp. 1-21
Author(s):  
Jorge San Martín ◽  
Erica L. Schwindt ◽  
Takéo Takahashi
Keyword(s):  
Incompressible Fluid ◽  
Stokes System ◽  
Partial Information ◽  
Viscous Incompressible Fluid ◽  
Rigid Bodies ◽  
Navier Stokes ◽  
Fluid Structure ◽  
Structure System ◽  
Spherical Waves ◽  
Enclosure Method

AbstractWe consider the geometrical inverse problem consisting in recovering an unknown obstacle in a viscous incompressible fluid by measurements of the Cauchy force on the exterior boundary. We deal with the case where the fluid equations are the nonstationary Stokes system and using the enclosure method, we can recover the convex hull of the obstacle and the distance from a point to the obstacle. With the same method, we can obtain the same result in the case of a linear fluid-structure system composed by a rigid body and a viscous incompressible fluid. We also tackle the corresponding nonlinear systems: the Navier–Stokes system and a fluid-structure system with free boundary. Using complex spherical waves, we obtain some partial information on the distance from a point to the obstacle.

Time delay and Lagrangian approximation for Navier–Stokes flow

Analysis ◽  
2015 ◽  
Vol 35 (4) ◽  
Author(s):  
Nazgul Asanalieva ◽  
Carolin Heutling ◽  
Werner Varnhorn
Keyword(s):  
Fluid Flow ◽  
Time Delay ◽  
Incompressible Fluid ◽  
Stokes Flow ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Navier Stokes ◽  
Incompressible Fluid Flow ◽  
Navier Stokes Equations

AbstractWe consider the nonstationary nonlinear Navier–Stokes equations describing the motion of a viscous incompressible fluid flow for

scholarly journals Numerical simulation of the flow of viscous incompressible fluid through cylindrical cavities

2019 ◽  
pp. 218-221
Author(s):  
Ya. P. Trotsenko
Keyword(s):  
Incompressible Fluid ◽  
Shear Layer ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Oscillation Mode ◽  
Navier Stokes ◽  
Sustained Oscillation ◽  
Tvd Scheme ◽  
Algebraic Equations ◽  
Linear Algebraic Equations

The flow of viscous incompressible fluid in a cylindrical duct with two serial diaphragms is studied by the numerical solution of the unsteady Navier–Stokes equations. The discretization procedure is based on the finite volume method using the TVD scheme for the discretization of the convective terms and second order accurate in both space and time difference schemes. The resulting system of non-linear algebraic equations is solved by the PISO algorithm. It is shown that the fluid flow in the region between the diaphragms is nonstationary and is characterized by the presence of an unstable shear layer under certain parameters. A series of ring vortices is formed in the shear layer that causes quasi-periodic self-sustained oscillations of the velocity and pressure fields in the orifice of the second diaphragm. There can be four self-sustained oscillation modes depending on the length of the cavity formed by the diaphragms. With the increase in the distance between the diaphragms, the frequency of oscillations decreases within the same self-oscillation mode and rises sharply with the switch to the next mode.

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