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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00492748" target="_blank" >RIV/67985840:_____/19:00492748 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.nonrwa.2018.07.029" target="_blank" >http://dx.doi.org/10.1016/j.nonrwa.2018.07.029</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.nonrwa.2018.07.029" target="_blank" >10.1016/j.nonrwa.2018.07.029</a>

Result language
angličtina
Original language name
Structure of the set of stationary solutions to the equations of motion of a class of generalized Newtonian fluids
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA17-01747S" target="_blank" >GA17-01747S: Theory and numerical analysis of coupled problems in fluid dynamics</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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