Structure of the set of stationary solutions to the equations of motion of a class of generalized Newtonian fluids

We investigate the steady-state equations of motion of the generalized Newtonian fluid in a bounded domain Ω⊂RN, when N=2 or N=3. Applying the tools of nonlinear analysis (Smale’s theorem, theory of Fredholm operators, etc.), we show that if the dynamic stress tensor has the 2-structure then the sol...

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Bibliographic Details
Published in:Nonlinear analysis: real world applications 2019-02, Vol.45, p.704-720
Main Authors: Neustupa, Jiří, Siginer, Dennis A.
Format: Article
Language:English
Subjects:
Equations of motion
Equations of state
Generalized Newtonian fluid
Linear equations
Mathematical analysis
Newtonian fluids
Non-Newtonian fluids
Nonlinear analysis
Operators
Stationary solutions
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Summary:We investigate the steady-state equations of motion of the generalized Newtonian fluid in a bounded domain Ω⊂RN, when N=2 or N=3. Applying the tools of nonlinear analysis (Smale’s theorem, theory of Fredholm operators, etc.), we show that if the dynamic stress tensor has the 2-structure then the solution set is finite and the solutions are C1-functions of the external volume force f for generic f. We also derive a series of properties of related operators in the case of a more general p-structure, show that the solution set is compact if p>3N∕(N+2) and explain why the same approach as in the case p=2 cannot be applied if p≠2.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2018.07.029