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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

  • Czech description

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