scholarly journals A Note on the Pressure of Strong Solutions to the Stokes System in Bounded and Exterior Domains

2017 ◽  
Vol 20 (2) ◽  
pp. 721-731
Author(s):  
Jörg Wolf
Keyword(s):  
Stokes System ◽  
Strong Solutions ◽  
Exterior Domains

scholarly journals Asymptotics of solutions to the Navier-Stokes system in exterior domains

2014 ◽  
Vol 90 (3) ◽  
pp. 785-806 ◽  
Author(s):  
Dragoş Iftimie ◽  
Grzegorz Karch ◽  
Christophe Lacave
Keyword(s):  
Stokes System ◽  
Navier Stokes ◽  
Exterior Domains ◽  
Asymptotics Of Solutions

Strong solutions to the density-dependent incompressible Cahn–Hilliard–Navier–Stokes system

2019 ◽  
Vol 16 (04) ◽  
pp. 701-742 ◽  
Author(s):  
Xiaopeng Zhao
Keyword(s):  
Stokes System ◽  
Initial Density ◽  
Local Existence ◽  
Strong Solutions ◽  
Incompressible Fluids ◽  
Navier Stokes ◽  
Initial Value ◽  
Two Phase ◽  
Density Dependent ◽  
Local Existence And Uniqueness

We study the density-dependent incompressible Cahn–Hilliard–Navier–Stokes system, which describes a two-phase flow of two incompressible fluids with different densities. We establish the local existence and uniqueness of strong solutions to the initial value problem in a bounded domain, when the initial density function enjoys a positive lower bound.

scholarly journals ON COUPLED PROBLEMS FOR VISCOUS FLOW IN EXTERIOR DOMAINS

1998 ◽  
Vol 08 (04) ◽  
pp. 657-684 ◽  
Author(s):  
M. FEISTAUER ◽  
C. SCHWAB
Keyword(s):  
Stokes Flow ◽  
Stokes System ◽  
Stokes Problem ◽  
Large Data ◽  
Transmission Conditions ◽  
Navier Stokes ◽  
Coupled Problems ◽  
Exterior Domains ◽  
Existence Of A Solution ◽  
Coupled Problem

The use of the complete Navier–Stokes system in an unbounded domain is not always convenient in computations and, therefore, the Navier–Stokes problem is often truncated to a bounded domain. In this paper we simulate the interaction between the flow in this domain and the exterior flow with the aid of a coupled problem. We propose in particular a linear approximation of the exterior flow (here the Stokes flow or potential flow) coupled with the interior Navier–Stokes problem via suitable transmission conditions on the artificial interface between the interior and exterior domains. Our choice of the transmission conditions ensures the existence of a solution of the coupled problem, also for large data.

The resolvent problem for the Stokes system in exterior domains: uniqueness and non-regularity in Hölder spaces

1992 ◽  
Vol 122 (1-2) ◽  
pp. 1-10 ◽  
Author(s):  
Paul Deuring
Keyword(s):  
Boundary Conditions ◽  
Existence Result ◽  
Stokes System ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Exterior Domains ◽  
Hölder Spaces ◽  
Image Position ◽  
Holder Spaces ◽  
Resolvent Problem

SynopsisWe consider the resolvent problem for the Stokes system in exterior domains, under Dirichlet boundary conditions:where Ω is a bounded domain in ℝ3. It will be shown that in general there is no constant C > 0 such that for with , div u = 0, and for with . However, if a solution (u, π) of problem (*) exists, it is uniquely determined, provided that u(x) and ∇π(x) decay for large values of |x|. These assertions imply a non-existence result in Hölder spaces.

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