Incompressible limit of a fluid-particle interaction model

Hongli Wang; Jianwei Yang

Applications of Mathematics (2021)

  • Volume: 66, Issue: 1, page 69-86
  • ISSN: 0862-7940

Abstract

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The incompressible limit of the weak solutions to a fluid-particle interaction model is studied in this paper. By using the relative entropy method and refined energy analysis, we show that, for well-prepared initial data, the weak solutions of the compressible fluid-particle interaction model converge to the strong solution of the incompressible Navier-Stokes equations as long as the Mach number goes to zero. Furthermore, the desired convergence rates are also obtained.

How to cite

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Wang, Hongli, and Yang, Jianwei. "Incompressible limit of a fluid-particle interaction model." Applications of Mathematics 66.1 (2021): 69-86. <http://eudml.org/doc/297075>.

@article{Wang2021,
abstract = {The incompressible limit of the weak solutions to a fluid-particle interaction model is studied in this paper. By using the relative entropy method and refined energy analysis, we show that, for well-prepared initial data, the weak solutions of the compressible fluid-particle interaction model converge to the strong solution of the incompressible Navier-Stokes equations as long as the Mach number goes to zero. Furthermore, the desired convergence rates are also obtained.},
author = {Wang, Hongli, Yang, Jianwei},
journal = {Applications of Mathematics},
keywords = {incompressible limit; relative entropy method; fluid-particle interaction model; incompressible Navier-Stokes equation},
language = {eng},
number = {1},
pages = {69-86},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Incompressible limit of a fluid-particle interaction model},
url = {http://eudml.org/doc/297075},
volume = {66},
year = {2021},
}

TY - JOUR
AU - Wang, Hongli
AU - Yang, Jianwei
TI - Incompressible limit of a fluid-particle interaction model
JO - Applications of Mathematics
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 1
SP - 69
EP - 86
AB - The incompressible limit of the weak solutions to a fluid-particle interaction model is studied in this paper. By using the relative entropy method and refined energy analysis, we show that, for well-prepared initial data, the weak solutions of the compressible fluid-particle interaction model converge to the strong solution of the incompressible Navier-Stokes equations as long as the Mach number goes to zero. Furthermore, the desired convergence rates are also obtained.
LA - eng
KW - incompressible limit; relative entropy method; fluid-particle interaction model; incompressible Navier-Stokes equation
UR - http://eudml.org/doc/297075
ER -

References

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  1. Ballew, J., Trivisa, K., 10.1090/S0033-569X-2012-01310-2, Q. Appl. Math. 70 (2012), 469-494. (2012) Zbl1418.76045MR2986131DOI10.1090/S0033-569X-2012-01310-2
  2. Ballew, J., Trivisa, K., 10.1016/j.na.2013.06.002, Nonlinear Anal., Theory Methods Appl., Ser. A 91 (2013), 1-19. (2013) Zbl1284.35303MR3081207DOI10.1016/j.na.2013.06.002
  3. Baranger, C., Boudin, L., Jabin, P.-E., Mancini, S., 10.1051/proc:2005004, ESAIM, Proc. 14 (2005), 41-47. (2005) Zbl1075.92031MR2226800DOI10.1051/proc:2005004
  4. Veiga, H. Beirão da, 10.1007/BF00387711, Arch. Ration. Mech. Anal. 128 (1994), 313-327. (1994) Zbl0829.76073MR1308856DOI10.1007/BF00387711
  5. Berres, S., Bürger, R., Karlsen, K. H., Tory, E. M., 10.1137/S0036139902408163, SIAM J. Appl. Math. 64 (2003), 41-80. (2003) Zbl1047.35071MR2029124DOI10.1137/S0036139902408163
  6. Carrillo, J. A., Goudon, T., 10.1080/03605300500394389, Commun. Partial Differ. Equations 31 (2006), 1349-1379. (2006) Zbl1105.35088MR2254618DOI10.1080/03605300500394389
  7. Carrillo, J. A., Karper, T., Trivisa, K., 10.1016/j.na.2010.12.031, Nonlinear Anal., Theory Methods Appl., Ser. A 74 (2011), 2778-2801. (2011) Zbl1214.35068MR2776527DOI10.1016/j.na.2010.12.031
  8. Chemin, J.-Y., Masmoudi, N., 10.1137/S0036141099359317, SIAM J. Math. Anal. 33 (2001), 84-112. (2001) Zbl1007.76003MR1857990DOI10.1137/S0036141099359317
  9. Chen, Y., Ding, S., Wang, W., 10.3934/dcds.2016032, Discrete Contin. Dyn. Syst. 36 (2016), 5287-5307. (2016) Zbl1353.35222MR3543548DOI10.3934/dcds.2016032
  10. Chen, Z.-M., Zhai, X., 10.1007/s00021-019-0428-3, J. Math. Fluid Mech. 21 (2019), Article ID 26, 23 pages. (2019) Zbl1416.35181MR3935027DOI10.1007/s00021-019-0428-3
  11. Constantin, P., Masmoudi, N., 10.1007/s00220-007-0384-2, Commun. Math. Phys. 278 (2008), 179-191. (2008) Zbl1147.35069MR2367203DOI10.1007/s00220-007-0384-2
  12. Danchin, R., Mucha, P. B., 10.1016/j.aim.2017.09.025, Adv. Math. 320 (2017), 904-925. (2017) Zbl1384.35058MR3709125DOI10.1016/j.aim.2017.09.025
  13. Donatelli, D., Feireisl, E., Novotný, A., 10.3934/dcdsb.2010.13.783, Discrete Contin. Dyn. Syst., Ser. B 13 (2010), 783-798. (2010) Zbl1194.35304MR2601340DOI10.3934/dcdsb.2010.13.783
  14. Evje, S., Wen, H., Zhu, C., 10.1142/S0218202517500038, Math. Models Methods Appl. Sci. 27 (2017), 323-346. (2017) Zbl1359.76291MR3606958DOI10.1142/S0218202517500038
  15. Feireisl, E., Petcu, M., 10.1016/j.jde.2019.03.006, J. Differ. Equation 267 (2019), 1836-1858. (2019) Zbl1416.35204MR3945619DOI10.1016/j.jde.2019.03.006
  16. Hsiao, L., Ju, Q., Li, F., 10.1007/s11401-008-0039-4, Chin. Ann. Math., Ser. B 30 (2009), 17-26. (2009) Zbl1181.35171MR2480811DOI10.1007/s11401-008-0039-4
  17. Huang, B., Huang, J., Wen, H., 10.1063/1.5089229, J. Math. Phys. 60 (2019), Article ID 061501, 20 pages. (2019) Zbl07082295MR3963486DOI10.1063/1.5089229
  18. Huang, F., Wang, D., Yuan, D., 10.3934/dcds.2019146, Discrete Contin. Dyn. Syst. 39 (2019), 3535-3575. (2019) Zbl1415.76638MR3959440DOI10.3934/dcds.2019146
  19. Klainerman, S., Majda, A., 10.1002/cpa.3160350503, Commun. Pure Appl. Math. 35 (1982), 629-651. (1982) Zbl0478.76091MR0668409DOI10.1002/cpa.3160350503
  20. Lin, C.-K., 10.1080/03605309508821108, Commun. Partial Differ. Equations 20 (1995), 677-707. (1995) Zbl0816.35105MR1318085DOI10.1080/03605309508821108
  21. Lions, P.-L., Mathematical Topics in Fluid Mechanics. Vol. 2: Compressible Models, Oxford Lecture Series in Mathematics and Its Applications 10. Clarendon Press, Oxford (1998). (1998) Zbl0908.76004MR1637634
  22. Lions, P.-L., Masmoudi, N., 10.1016/S0021-7824(98)80139-6, J. Math. Pures Appl., IX. Sér 77 (1998), 585-627. (1998) Zbl0909.35101MR1628173DOI10.1016/S0021-7824(98)80139-6
  23. Masmoudi, N., 10.1016/S0021-7824(98)80139-6, Ann. Inst. Henri Poincaré, Anal. Non linéaire 18 (2001), 199-224. (2001) Zbl0991.35058MR1808029DOI10.1016/S0021-7824(98)80139-6
  24. Ou, Y., 10.1016/j.jde.2009.05.009, J. Differ. Equations 247 (2009), 3295-3314. (2009) Zbl1181.35177MR2571578DOI10.1016/j.jde.2009.05.009
  25. Vauchelet, N., Zatorska, E., 10.1016/j.na.2017.07.003, Nonlinear Anal., Theory Methods Appl., Ser. A 163 (2017), 34-59. (2017) Zbl1370.35234MR3695967DOI10.1016/j.na.2017.07.003
  26. Vinkovic, I., Aguirre, C., Simoëns, S., Gorokhovski, M., 10.1016/j.ijmultiphaseflow.2005.10.005, Int. J. Multiphase Flow 32 (2006), 344-364. (2006) Zbl1135.76570DOI10.1016/j.ijmultiphaseflow.2005.10.005
  27. Williams, F. A., 10.1063/1.1724379, Phys. Fluids 1 (1958), 541-545. (1958) Zbl0086.41102DOI10.1063/1.1724379
  28. Williams, F. A., 10.1201/9780429494055, CRC Press, Boca Raton (1985). (1985) DOI10.1201/9780429494055

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