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Stability and Bifurcation in Viscous Incompressible Fluids
 

Summary: Stability and Bifurcation in Viscous
Incompressible Fluids
Herbert Amann
1 The Problem
We consider the motion of a viscous incompressible uid in a bounded
smooth
domain
of R 3 . It is governed by the laws of conservation of mass,
momentum, and energy given by
r  v = 0 ;
@ t v + (v  r)v = rp+r  S + b ;
c(@ t  + v  r) = r  q + S : D + r ;
(1:1)
respectively (e.g., [24], [27]). Here the velocity vector eld v, the pressure p,
and the absolute temperature  are the unknowns. The density has been
normalized to 1, and S is the viscous part of the stress tensor, b = b(x; t; )
is the body force, c = c() > 0 is the heat capacity, q is the heat ux vector,
D := D(v) :=
1
2

  

Source: Amann, Herbert - Institut für Mathematik, Universität Zürich

 

Collections: Mathematics