The Rayleigh-Bénard problem for compressible fluid flows
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00567885" target="_blank" >RIV/67985840:_____/23:00567885 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00205-022-01837-6" target="_blank" >https://doi.org/10.1007/s00205-022-01837-6</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00205-022-01837-6" target="_blank" >10.1007/s00205-022-01837-6</a>
Alternative languages
Result language
angličtina
Original language name
The Rayleigh-Bénard problem for compressible fluid flows
Original language description
We consider the physically relevant fully compressible setting of the Rayleigh-Bénard problem of a fluid confined between two parallel plates, heated from the bottom, and subjected to gravitational force. Under suitable restrictions imposed on the constitutive relations we show that this open system is dissipative in the sense of Levinson, meaning there exists a bounded absorbing set for any global-in-time weak solution. In addition, global-in-time trajectories are asymptotically compact in suitable topologies and the system possesses a global compact trajectory attractor A. The standard technique of Krylov and Bogolyubov then yields the existence of an invariant measure - a stationary statistical solution sitting on A. In addition, the Birkhoff-Khinchin ergodic theorem provides convergence of ergodic averages of solutions belonging to A a.s. with respect to the invariant measure.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA21-02411S" target="_blank" >GA21-02411S: Solving ill posed problems in the dynamics of compressible fluids</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Archive for Rational Mechanics and Analysis
ISSN
0003-9527
e-ISSN
1432-0673
Volume of the periodical
247
Issue of the periodical within the volume
1
Country of publishing house
DE - GERMANY
Number of pages
31
Pages from-to
9
UT code for WoS article
000917250800001
EID of the result in the Scopus database
2-s2.0-85146628525