A Weak Solution to the Navier–Stokes System with Navier’s Boundary Condition in a Time-Varying Domain

2016 ◽  
pp. 375-400 ◽  
Author(s):  
Jiří Neustupa ◽  
Patrick Penel
Keyword(s):  
Boundary Condition ◽  
Weak Solution ◽  
Stokes System ◽  
Navier Stokes ◽  
Time Varying

scholarly journals On the Solvability of a Problem of Stationary Fluid Flow in a Helical Pipe

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
Author(s):  
Igor Pažanin
Keyword(s):  
Boundary Condition ◽  
Weak Solution ◽  
Fluid Flow ◽  
Existence And Uniqueness ◽  
Stokes System ◽  
Navier Stokes ◽  
Small Data ◽  
Helical Pipe ◽  
Pressure Boundary Condition ◽  
Incompressible Newtonian Fluid

We consider a flow of incompressible Newtonian fluid through a pipe with helical shape. We suppose that the flow is governed by the prescribed pressure drop between pipe's ends. Such model has relevance to some important engineering applications. Under small data assumption, we prove the existence and uniqueness of the weak solution to the corresponding Navier-Stokes system with pressure boundary condition. The proof is based on the contraction method.

ON THE ROBIN PROBLEM FOR STOKES AND NAVIER–STOKES SYSTEMS

2006 ◽  
Vol 16 (05) ◽  
pp. 701-716 ◽  
Author(s):  
REMIGIO RUSSO ◽  
ALFONSINA TARTAGLIONE
Keyword(s):  
Boundary Layer ◽  
Weak Solution ◽  
Lipschitz Domain ◽  
Stokes System ◽  
Navier Stokes ◽  
Robin Problem ◽  
Layer Potentials ◽  
Very Weak Solution ◽  
Stokes Systems ◽  
Compact Boundary

The Robin problem for Stokes and Navier–Stokes systems is considered in a Lipschitz domain with a compact boundary. By making use of the boundary layer potentials approach, it is proved that for Stokes system this problem admits a very weak solution under suitable assumptions on the boundary datum. A similar result is proved for the Navier–Stokes system, provided that the datum is "sufficiently small".

scholarly journals Stationary Navier–Stokes equations with non-homogeneous boundary condition in a system of two connected layers

2012 ◽  
Vol 53 ◽  
Author(s):  
Kristina Kaulakytė
Keyword(s):  
Boundary Condition ◽  
Boundary Problem ◽  
Stokes System ◽  
Stokes Equations ◽  
Boundary Value ◽  
Homogeneous Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stationary Navier Stokes Equations

In this paper the stationary Navier–Stokes system with non-homogeneous boundary condition is studied in domain which consists of two connected layers. The extension of the boundary value, which reduces the non-homogeneous boundary problem to the homogeneous one, is constructed in this paper.

scholarly journals Self-propelled motion of a rigid body inside a density dependent incompressible fluid

2020 ◽  
Author(s):  
Sarka Necasova ◽  
Mythily Ramaswamy ◽  
Arnab Roy ◽  
Anja Schlomerkemper
Keyword(s):  
Angular Momentum ◽  
Weak Solution ◽  
Global Existence ◽  
Viscous Fluid ◽  
Rigid Body ◽  
Incompressible Fluid ◽  
Stokes System ◽  
Navier Stokes ◽  
Navier Condition ◽  
Whole Space

This paper is devoted to the existence of a weak solution to a system describing a self-propelled motion of a rigid body in a viscous fluid in the whole space. The fluid is modelled by the incompressible nonhomogeneous Navier-Stokes system with a nonnegative density. The motion of the rigid body is described by the  balance of linear and angular momentum. We consider the case where slip is allowed at the fluid-solid interface through Navier condition and prove the global existence of a weak solution.

scholarly journals ON THE SENSITIVITY OF THE NONLINEAR TERM IN THE OUTFLOW BOUNDARY CONDITION

2021 ◽  
Vol 61 (SI) ◽  
pp. 117-121
Author(s):  
Tomáš Neustupa ◽  
Ondřej Winter
Keyword(s):  
Boundary Condition ◽  
Fluid Flow ◽  
Kinetic Energy ◽  
Stokes System ◽  
Nonlinear Term ◽  
Navier Stokes ◽  
Outflow Boundary Condition ◽  
Flow Through ◽  
Outflow Boundary

This paper studies the artificial outflow boundary condition for the Navier-Stokes system. This type of condition is widely used and it is therefore very important to study its influence on a numerical solution of the corresponding boundary-value problem. We particularly focus on the role of the coefficient in front of the nonlinear term in the boundary condition on the outflow. The influence of this term is examined numerically, comparing the obtained results in a close neighbourhood of the outflow. The numerical experiment is carried out for a fluid flow through the channel with so called sudden extension. Presented numerical results are obtained by means of the OpenFOAM toolbox. They confirm that the kinetic energy of the flow in the channel can be controlled by means of the proposed boundary condition.

scholarly journals Global existence for a two-species chemotaxis-Navier-Stokes system with $ p $-Laplacian

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jiayi Han ◽  
Changchun Liu
Keyword(s):  
Weak Solution ◽  
Global Existence ◽  
Stokes System ◽  
Three Dimensional ◽  
Global Weak Solution ◽  
Navier Stokes ◽  
Bounded Domains

<p style='text-indent:20px;'>We consider a two-species chemotaxis-Navier-Stokes system with <inline-formula><tex-math id="M2">\begin{document}$ p $\end{document}</tex-math></inline-formula>-Laplacian in three-dimensional smooth bounded domains. It is proved that for any <inline-formula><tex-math id="M3">\begin{document}$ p\geq2 $\end{document}</tex-math></inline-formula>, the problem admits a global weak solution.</p>

Global weak solutions in a three-dimensional Keller–Segel–Navier–Stokes system with subcritical sensitivity

2017 ◽  
Vol 27 (14) ◽  
pp. 2745-2780 ◽  
Author(s):  
Yulan Wang
Keyword(s):  
Weak Solution ◽  
Stokes System ◽  
Three Dimensional ◽  
Solution Concept ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Global Solvability ◽  
Navier Stokes ◽  
Fluid Equation ◽  
Free System

This paper deals with the Keller–Segel–Navier–Stokes system [Formula: see text] in a bounded domain [Formula: see text] with smooth boundary, where [Formula: see text] and [Formula: see text] are given functions. We shall develop a weak solution concept which requires solutions to satisfy very mild regularity hypotheses only, especially for the component [Formula: see text]. Under the assumption that there exist [Formula: see text] and [Formula: see text] such that [Formula: see text] it is finally shown that for all suitably regular initial data an associated initial-boundary value problem possesses a globally defined weak solution. In comparison to the result for the corresponding fluid-free system, it is easy to see that the restriction on [Formula: see text] here is optimal. This result extends previous studies on global solvability for this system in the two-dimensional domain and for the associated chemotaxis-Stokes system obtained on neglecting the nonlinear convective term in the fluid equation.

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