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

0492748 - MÚ 2020 RIV GB eng J - Journal Article
Neustupa, Jiří - Siginer, D.
Structure of the set of stationary solutions to the equations of motion of a class of generalized Newtonian fluids.
Nonlinear Analysis: Real World Applications. Roč. 45, February (2019), s. 704-720. ISSN 1468-1218. E-ISSN 1878-5719
R&D Projects: GA ČR(CZ) GA17-01747S
Institutional support: RVO:67985840
Keywords : equations of motion * generalized Newtonian fluid * stationary solutions
OECD category: Pure mathematics
Impact factor: 2.072, year: 2019
Method of publishing: Limited access
http://dx.doi.org/10.1016/j.nonrwa.2018.07.029

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.
Permanent Link: http://hdl.handle.net/11104/0286128