Structure of the set of stationary solutions to the equations of motion of a class of generalized Newtonian fluids. (February 2019)

• Record Type: Journal Article
• Authors: Neustupa, Jiří; Siginer, Dennis A.
• Is Part Of: Nonlinear analysis. Volume 45(2019)
• Page Start: 704
• Page End: 720
• Publication Date: 2019-02
• Subjects: Generalized Newtonian fluid -- Equations of motion -- Stationary solutions; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.07.029
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We investigate the steady-state equations of motion of the generalized Newtonian fluid in a bounded domain Ω ⊂ 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 > 3 N ∕ ( N + 2 ) and explain why the same approach as in the case p = 2 cannot be applied if p ≠ 2 .