On the long-time behavior of solutions to the Navier-Stokes-Fourier system on unbounded domains

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00604368" target="_blank" >RIV/67985840:_____/25:00604368 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1112/jlms.70067" target="_blank" >https://doi.org/10.1112/jlms.70067</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/jlms.70067" target="_blank" >10.1112/jlms.70067</a>

Result language
angličtina
Original language name
On the long-time behavior of solutions to the Navier-Stokes-Fourier system on unbounded domains
Original language description
We consider the Navier-Stokes-Fourier (NSF) system on an unbounded domain in the Euclidean space R^3, supplemented by the far-field conditions for the phase variables, specifically: rho rightarrow 0, vartheta rightarrow varthetainfty, u rightarrow 0 as |x| rightarrow infty. We study the long-time behavior of solutions and we prove that any global-in-time weak solution to the NSF system approaches the equilibrium rho s = 0, vartheta s = varthetat infty, us=0 in the sense of ergodic averages for time tending to infinity. As a consequence of the convergence result combined with the total mass conservation, we can show that the total momentum of global-in-time weak solutions is never globally conserved.
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/GA24-11034S" target="_blank" >GA24-11034S: Dissipative systems in fluid dynamics</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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