Structure of the set of stationary solutions to the equations of motion of a class of generalized Newtonian fluids. (February 2019) - Neustupa, Jiří; Siginer, Dennis A.
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 .