Darcy's law as low Mach and homogenization limit of a compressible fluid in perforated domains
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10441256" target="_blank" >RIV/00216208:11320/21:10441256 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=cQlilzT31R" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=cQlilzT31R</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S0218202521500391" target="_blank" >10.1142/S0218202521500391</a>
Alternative languages
Result language
angličtina
Original language name
Darcy's law as low Mach and homogenization limit of a compressible fluid in perforated domains
Original language description
We consider the homogenization limit of the compressible barotropic Navier-Stokes equations in a three-dimensional domain perforated by periodically distributed identical particles. We study the regime of particle sizes and distances such that the volume fraction of particles tends to zero but their resistance density tends to infinity. Assuming that the Mach number is decreasing with a certain rate, the rescaled velocity and pressure of the microscopic system converges to the solution of an effective equation which is given by Darcy's law. The range of sizes of particles we consider is exactly the same which leads to Darcy's law in the homogenization limit of incompressible fluids. Unlike previous results for the Darcy regime we estimate the deficit related to the pressure approximation via the Bogovskii operator. This allows for more flexible estimates of the pressure in Lebesgue and Sobolev spaces and allows to proof convergence results for all barotropic exponents gamma > 3/2.
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
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematical Models and Methods in Applied Sciences
ISSN
0218-2025
e-ISSN
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Volume of the periodical
31
Issue of the periodical within the volume
09
Country of publishing house
SG - SINGAPORE
Number of pages
33
Pages from-to
1787-1819
UT code for WoS article
000698444200003
EID of the result in the Scopus database
2-s2.0-85112640168