Existence of stationary weak solutions for compressible heat conducting flows

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Existence of stationary weak solutions for compressible heat conducting flows

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Existence of stationary weak solutions for compressible heat conducting flows

Popis výsledku anglicky

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.

Druh

C - Kapitola v odborné knize

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA16-03230S" target="_blank" >GA16-03230S: Termodynamicky konzistentni modely pro proudění tekutin: matematická teorie a numerické řešení</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název knihy nebo sborníku

Handbook of mathematical analysis in mechanics of viscous fluids

ISBN

978-3-319-13343-0

Počet stran výsledku

68

Strana od-do

2595-2662

Počet stran knihy

3045

Název nakladatele

Springer International Publishing

Místo vydání

Neuveden

Kód UT WoS kapitoly

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