On quasi-stationary models of mixtures of compressible fluids

Jens Frehse; Wladimir Weigant

Applications of Mathematics (2008)

  • Volume: 53, Issue: 4, page 319-345
  • ISSN: 0862-7940

Abstract

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We consider mixtures of compressible viscous fluids consisting of two miscible species. In contrast to the theory of non-homogeneous incompressible fluids where one has only one velocity field, here we have two densities and two velocity fields assigned to each species of the fluid. We obtain global classical solutions for quasi-stationary Stokes-like system with interaction term.

How to cite

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Frehse, Jens, and Weigant, Wladimir. "On quasi-stationary models of mixtures of compressible fluids." Applications of Mathematics 53.4 (2008): 319-345. <http://eudml.org/doc/37787>.

@article{Frehse2008,
abstract = {We consider mixtures of compressible viscous fluids consisting of two miscible species. In contrast to the theory of non-homogeneous incompressible fluids where one has only one velocity field, here we have two densities and two velocity fields assigned to each species of the fluid. We obtain global classical solutions for quasi-stationary Stokes-like system with interaction term.},
author = {Frehse, Jens, Weigant, Wladimir},
journal = {Applications of Mathematics},
keywords = {compressible viscous fluids; miscible mixtures; quasi-stationary; compressible viscous fluids; miscible mixtures; quasi-stationary},
language = {eng},
number = {4},
pages = {319-345},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On quasi-stationary models of mixtures of compressible fluids},
url = {http://eudml.org/doc/37787},
volume = {53},
year = {2008},
}

TY - JOUR
AU - Frehse, Jens
AU - Weigant, Wladimir
TI - On quasi-stationary models of mixtures of compressible fluids
JO - Applications of Mathematics
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 4
SP - 319
EP - 345
AB - We consider mixtures of compressible viscous fluids consisting of two miscible species. In contrast to the theory of non-homogeneous incompressible fluids where one has only one velocity field, here we have two densities and two velocity fields assigned to each species of the fluid. We obtain global classical solutions for quasi-stationary Stokes-like system with interaction term.
LA - eng
KW - compressible viscous fluids; miscible mixtures; quasi-stationary; compressible viscous fluids; miscible mixtures; quasi-stationary
UR - http://eudml.org/doc/37787
ER -

References

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  1. Bernardi, Ch., Pironneau, O., 10.1080/03605309108820752, Commun. Partial Differential Equations 16 (1991), 59-104. (1991) Zbl0723.76033MR1096834DOI10.1080/03605309108820752
  2. Feireisl, E., 10.1006/jdeq.2001.4137, J. Differ. Equations 184 (2002), 97-108. (2002) Zbl1012.76079MR1929148DOI10.1006/jdeq.2001.4137
  3. Feireisl, E., Dynamics of Compressible Flow, Oxford University Press Oxford (2003). (2003) 
  4. Feireisl, E., Novotný, A., Petzeltová, H., 10.1007/PL00000976, J. Math. Fluid Mech. 3 (2001), 358-392. (2001) MR1867887DOI10.1007/PL00000976
  5. Frehse, J., Goj, S., Málek, J., 10.1137/S0036141003433425, SIAM J. Math. Anal. 36 (2005), 1259-1281 (electronic). (2005) Zbl1084.35057MR2139449DOI10.1137/S0036141003433425
  6. Frehse, J., Goj, S., Málek, J., 10.1007/s10492-005-0035-x, Appl. Math. 50 (2005), 527-541. (2005) Zbl1099.35079MR2181024DOI10.1007/s10492-005-0035-x
  7. Gagliardo, E., Ulteriori proprietà di alcune classi di funzioni in più variabili, Ric. Mat. 8 (1959), 24-51. (1959) Zbl0199.44701MR0109295
  8. Goj, S., Analysis for mixtures of fluids. Bonner Math. Schriften, Dissertation Universität Bonn, Math. Inst. (2005), http://bib.math.uni-bonn.de/pdf2/BMS-375.pdf. MR2205590
  9. Golovkin, K. K., On imbedding theorems, Soviet Math. Dokl. 1 (1960), 998-1001. (1960) Zbl0104.33102MR0121640
  10. Haupt, P., Continuum Mechanics Theory of Materials, 2nd ed. Advanced Texts in Physics, Springer Berlin (2002). (2002) MR2011110
  11. Il'in, V. P., On theorems of ``imbedding'', Trudy Mat. Inst. Steklov. 53 (1959), 359-386. (1959) MR0112930
  12. Kazhikhov, A. V., Resolution of boundary value problems for nonhomogeneous viscous fluids, Dokl. Akad. Nauk 216 (1974), 1008-1010 Russian. (1974) 
  13. Kazhikhov, A. V., 10.1007/BF00995131, Acta Appl. Math. 37 (1994), 77-81. (1994) Zbl0815.35083MR1308747DOI10.1007/BF00995131
  14. Ladyzhenskaya, O. A., Solonnikov, V. A., On the unique solvability of the initial value problem for viscous incompressible inhomogeneous fluids, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova (LOMI) 52 (1975), 52-109, 218-219 Russian. (1975) Zbl0376.76021
  15. Lions, P.-L., Mathematical Topics in Fluid Mechanics. Vol. 1: Compressible Models. Oxford Science Publications, Clarendon Press Oxford (1996). (1996) MR1422251
  16. Lions, P.-L., Mathematical Topics in Fluid Mechanics. Vol. 2: Compressible Models. Oxford Science Publications, Clarendon Press Oxford (1998). (1998) MR1637634
  17. Mamontov, A. E., 10.1007/BF02110728, Sib. Mat. Zh. 37 (1996), 1117-1131. (1996) Zbl0884.76077MR1643271DOI10.1007/BF02110728
  18. Nouri, A., Poupaud, F., Demay, Y., 10.1090/qam/1466141, Q. Appl. Math. 55 (1997), 421-435. (1997) Zbl0882.35091MR1466141DOI10.1090/qam/1466141
  19. Nouri, A., Poupaud, F., 10.1006/jdeq.1995.1139, J. Differ. Equations 122 (1995), 71-88. (1995) Zbl0842.35079MR1356130DOI10.1006/jdeq.1995.1139
  20. Rajagopal, K. R., Tao, L., Mechanics of Mixtures. Series on Advances in Mathematics for Applied Sciences Vol. 35, World Scientific Publishing River Edge (1995). (1995) MR1370661
  21. Solonnikov, V. A., On boundary value problems for linear parabolic systems of differential equations of general form, Trudy Mat. Inst. Steklov 83 (1965), 3-163. (1965) Zbl0164.12502MR0211083
  22. Solonnikov, V. A., On the solvability of the initial-boundary problem for the equations of motion of a viscous compressible fluid, Zap. Nauchn. Semin. Leningrad, Otd. Mat. Inst. Steklova (LOMI) 56 (1976), 128-142. (1976) MR0481666
  23. Tani, A., 10.2977/prims/1195190106, Publ. Res. Inst. Math. Sci., Kyoto Univ. 13 (1977), 193-253. (1977) Zbl0366.35070DOI10.2977/prims/1195190106
  24. Vaigant, V. A., Kazhikhov, A. V., Global solutions of equations of potential flows of a compressible viscous fluid for small Reynolds numbers, Differentsial'nye Uravneniya 30 (1994), 1010-1022. (1994) MR1312722
  25. Yudovich, V. I., Nichtstationäre Strömung einer idealen inkompressiblen Flüssigkeit, Zh. Vychisl. Mat. Fiz. 3 (1963), 1032-1066 Russian. (1963) Zbl0129.19402
  26. Yudovich, V. I., Linearization Method in the Hydrodynamic Stability Theory, Izdatel'stvo Rostovskogo Universiteta Rostov (1984), Russian. (1984) Zbl0553.76038

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