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

    Abstract

    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
    Volume45
    DOIs
    Publication statusPublished - Feb 2019

    Fingerprint

    Newtonian Fluid
    Stationary Solutions
    Solution Set
    Equations of motion
    Equations of Motion
    Fredholm Operator
    Fluids
    Stress Tensor
    State Equation
    Nonlinear Analysis
    Bounded Domain
    Nonlinear analysis
    Tensors
    Series
    Mathematical operators
    Operator
    Theorem
    Class

    All Science Journal Classification (ASJC) codes

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

    Cite this

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