| Title:
|
Weak solutions for steady compressible Navier-Stokes-Fourier system in two space dimensions (English) |
| Author:
|
Novotný, Antonín |
| Author:
|
Pokorný, Milan |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
56 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
137-160 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider steady compressible Navier-Stokes-Fourier system in a bounded two-dimensional domain. We show the existence of a weak solution for arbitrarily large data for the pressure law $p(\varrho ,\vartheta ) \sim \varrho ^\gamma + \varrho \vartheta $ if $\gamma >1$ and $p(\varrho ,\vartheta ) \sim \varrho \ln ^\alpha (1+\varrho ) + \varrho \vartheta $ if $\gamma =1$, $\alpha >0$, depending on the model for the heat flux. (English) |
| Keyword:
|
steady compressible Navier-Stokes-Fourier system |
| Keyword:
|
weak solution |
| Keyword:
|
entropy inequality |
| Keyword:
|
Orlicz spaces |
| Keyword:
|
compensated compactness |
| Keyword:
|
renormalized solution |
| MSC:
|
35A01 |
| MSC:
|
35D30 |
| MSC:
|
35Q30 |
| MSC:
|
35Q35 |
| MSC:
|
76N10 |
| idZBL:
|
Zbl 1224.76108 |
| idMR:
|
MR2807430 |
| DOI:
|
10.1007/s10492-011-0013-4 |
| . |
| Date available:
|
2011-01-03T14:58:47Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141410 |
| . |
| Reference:
|
[1] Erban, R.: On the existence of solutions to the Navier-Stokes equations of a two-dimensional compressible flow.Math. Methods Appl. Sci. 26 (2003), 489-517. Zbl 1061.76073, MR 1965718, 10.1002/mma.362 |
| Reference:
|
[2] Feireisl, E., Novotný, A.: Singular Limits in Thermodynamics of Viscous Fluids. Advances in Mathematical Fluid Mechanics.Birkhäuser Basel (2009). MR 2499296 |
| Reference:
|
[3] Frehse, J., Steinhauer, M., Weigant, W.: The Dirichlet Problem for Steady Viscous Compressible Flow in 3-D.Preprint University of Bonn, SFB 611, No. 347 (2007), http://www.iam.uni-bonn.de/sfb611/. |
| Reference:
|
[4] Frehse, J., Steinhauer, M., Weigant, W.: The Dirichlet problem for viscous compressible isothermal Navier-Stokes equations in two-dimensions.Arch. Ration. Mech. Anal. 198 (2010), 1-12. Zbl 1229.35175, MR 2679367, 10.1007/s00205-010-0338-2 |
| Reference:
|
[5] Kufner, A., John, O., Fučík, S.: Function spaces.Academia Praha (1977). MR 0482102 |
| Reference:
|
[6] Lions, P.-L.: Mathematical Topics in Fluid Dynamics, Vol. 2: Compressible Models. Oxford Lecture Series in Mathematics and Its Applications, Vol. 10.Clarendon Press Oxford (1998). MR 1637634 |
| Reference:
|
[7] Maligranda, L.: Orlicz Spaces and Interpolation.Univ. Estadual de Campinas Campinas (1989). Zbl 0874.46022, MR 2264389 |
| Reference:
|
[8] Mucha, P. B., Pokorný, M.: On the steady compressible Navier-Stokes-Fourier system.Commun. Math. Phys. 288 (2009), 349-377. Zbl 1172.35467, MR 2491627, 10.1007/s00220-009-0772-x |
| Reference:
|
[9] Mucha, P. B., Pokorný, M.: Weak solutions to equations of steady compressible heat conducting fluids.Math. Models Methods Appl. Sci. 20 (2010), 785-813. Zbl 1191.35207, MR 2652619, 10.1142/S0218202510004441 |
| Reference:
|
[10] Novotný, A., Pokorný, M.: Steady compressible Navier-Stokes-Fourier system for monoatomic gas and its generalizations.J. Differ. Equations Accepted. See also Preprint Series of Nečas Center for Mathematical Modeling, http://www.karlin.mff.cuni.cz/ncmm/research/Preprints/servirPrintsYY.php?y=2010. Preprint No. 2010-021. |
| Reference:
|
[11] Novotný, A., Pokorný, M.: Weak and variational solutions to steady equations for compressible heat conducting fluids.Submitted. See also Preprint Series of Nečas Center for Mathematical Modeling, http://www.karlin.mff.cuni.cz/ncmm/research/Preprints/servirPrintsYY.php?y=2010. Preprint No. 2010-023. |
| Reference:
|
[12] Novotný, A., Straškraba, I.: Introduction to the Mathematical Theory of Compressible Flow.Oxford University Press Oxford (2004). Zbl 1088.35051, MR 2084891 |
| Reference:
|
[13] Pecharová, P., Pokorný, M.: Steady compressible Navier-Stokes-Fourier system in two space dimensions.Commentat. Math. Univ. Carol (to appear). MR 2858268 |
| Reference:
|
[14] Plotnikov, P. I., Sokołowski, J.: On compactness, domain dependence and existence of steady state solutions to compressible isothermal Navier-Stokes equations.J. Math. Fluid Mech. 7 (2005), 529-573. Zbl 1090.35140, MR 2189674, 10.1007/s00021-004-0134-6 |
| Reference:
|
[15] Plotnikov, P. I., Sokołowski, J.: Concentrations of stationary solutions to compressible Navier-Stokes equations.Commun. Math. Phys. 258 (2005), 567-608. MR 2172011, 10.1007/s00220-005-1358-x |
| Reference:
|
[16] Plotnikov, P. I., Sokołowski, J.: Stationary solutions of Navier-Stokes equations for diatomic gases.Russ. Math. Surv. 62 (2007), 561-593. Zbl 1139.76049, MR 2355421, 10.1070/RM2007v062n03ABEH004414 |
| Reference:
|
[17] Vodák, R.: The problem $\div v=f$ and singular integrals on Orlicz spaces.Acta Univ. Palacki. Olomuc, Fac. Rerum Nat. Math. 41 (2002), 161-173. MR 1968228 |
| . |
