Structure of the set of stationary solutions to the equations of motion of a class of generalized Newtonian fluids
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Publication Details
Author list: Neustupa J, Siginer DA
Publisher: Elsevier
Place: OXFORD
Publication year: 2019
Journal: Nonlinear Analysis: Real World Applications (1468-1218)
Journal acronym: NONLINEAR ANAL-REAL
Volume number: 45
Start page: 704
End page: 720
Number of pages: 17
ISSN: 1468-1218
eISSN: 1878-5719
Languages: English-Great Britain (EN-GB)
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Abstract
We investigate the steady-state equations of motion of the generalized Newtonian fluid in a bounded domain Omega subset of R-N, 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 C-1-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 not equal 2. (C) 2018 Elsevier Ltd. All rights reserved.
Keywords
Equations of motion, Generalized Newtonian fluid, stationary solutions
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