Existence of stationary weak solutions for compressible heat conducting flows
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10388564" target="_blank" >RIV/00216208:11320/18:10388564 - isvavai.cz</a>
Result on the web
<a href="https://rd.springer.com/referenceworkentry/10.1007/978-3-319-13344-7_64" target="_blank" >https://rd.springer.com/referenceworkentry/10.1007/978-3-319-13344-7_64</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-319-13344-7_64" target="_blank" >10.1007/978-3-319-13344-7_64</a>
Alternative languages
Result language
angličtina
Original language name
Existence of stationary weak solutions for compressible heat conducting flows
Original language description
The steady compressible Navier-Stokes-Fourier system is considered, with either Dirichlet or Navier boundary conditions for the velocity and the heat flux on the boundary proportional to the difference of the temperature inside and outside. In dependence on several parameters, i.e., the adiabatic constant appearing in the pressure law p.%; #/ % C %# and the growth exponent in the heat conductivity, i.e., .#/ .1 C #m/, and without any restriction on the size of the data, the main ideas of the construction of weak and variational entropy solutions for the three-dimensional flows with temperature-dependent viscosity coefficients are explained. Further, the case when it is possible to prove existence of solutions with bounded density is reviewed. The main changes in the construction of solutions for the two-dimensional flows are mentioned, and finally, results for more complex systems are reviewed, where the steady compressible Navier-Stokes-Fourier equations play an important role.
Czech name
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Czech description
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Classification
Type
C - Chapter in a specialist book
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA16-03230S" target="_blank" >GA16-03230S: Thermodynamically consistent models for fluid flows: mathematical theory and numerical solution</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Book/collection name
Handbook of mathematical analysis in mechanics of viscous fluids
ISBN
978-3-319-13343-0
Number of pages of the result
68
Pages from-to
2595-2662
Number of pages of the book
3045
Publisher name
Springer International Publishing
Place of publication
Neuveden
UT code for WoS chapter
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