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

Jiří Neustupa, Siginer Dennis

Research output: Contribution to journalArticle


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.

Original languageEnglish
Pages (from-to)704-720
Number of pages17
JournalNonlinear Analysis: Real World Applications
Publication statusPublished - Feb 2019


All Science Journal Classification (ASJC) codes

  • Analysis
  • Engineering(all)
  • Economics, Econometrics and Finance(all)
  • Computational Mathematics
  • Applied Mathematics

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