scholarly journals On the Stokes problem in exterior domains: The maximum modulus theorem

2014 ◽  
Vol 34 (5) ◽  
pp. 2135-2171 ◽  
Author(s):  
Paolo Maremonti ◽  
Keyword(s):  
Stokes Problem ◽  
Maximum Modulus ◽  
Exterior Domains ◽  
Maximum Modulus Theorem

ON THE MAXIMUM MODULUS THEOREM IN LINEAR ELASTOSTATICS FOR EXTERIOR DOMAINS

1996 ◽  
Vol 06 (06) ◽  
pp. 721-728
Author(s):  
GIULIO STARITA
Keyword(s):  
Positive Constant ◽  
Three Dimensional ◽  
Maximum Modulus ◽  
Finite Energy ◽  
Exterior Domains ◽  
Dirichlet Data ◽  
Maximum Value ◽  
Linear Elastostatics ◽  
Maximum Modulus Theorem

This paper deals with the system of linear elastostatics in exterior three-dimensional domains. We prove that the modulus of every solution with finite energy of such a system may be majorized by a positive constant times the maximum value of the modulus of the Dirichlet data at the boundary (maximum modulus theorem).

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.

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