Regularity results for electrorheological fluids: the stationary case

Emilio Acerbi; Giuseppe Mingione

doi:10.1016/S1631-073X(02)02337-3

Regularity results for electrorheological fluids: the stationary case
[Résultats de régularité pour les fluides électrorhéologiques : le cas stationnaire]

Emilio Acerbi ¹ ; Giuseppe Mingione ¹

¹ Dipartimento di Matematica, Via D'Azeglio, 85, 43100 Parma, Italie

Comptes Rendus. Mathématique, Volume 334 (2002) no. 9, pp. 817-822

Abstract (VO)
Résumé

We report on some regularity results for weak solutions to systems modelling electrorheological fluids in the stationary case, as proposed in [8].

On prouve des résultats de régularité pour les solutions faibles de systèmes modélisant les fluides électrorhéologiques dans le cas stationnaire, utilisant le modèle introduit dans [8].

Reçu le : 2001-10-09
Accepté le : 2002-02-28
Publié le : 2002-01-01

DOI : 10.1016/S1631-073X(02)02337-3

Affiliations des auteurs :

Emilio Acerbi ¹ ; Giuseppe Mingione ¹

¹ Dipartimento di Matematica, Via D'Azeglio, 85, 43100 Parma, Italie

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     title = {Regularity results for electrorheological fluids: the stationary case},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {817--822},
     year = {2002},
     publisher = {Elsevier},
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     number = {9},
     doi = {10.1016/S1631-073X(02)02337-3},
     language = {en},
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Emilio Acerbi; Giuseppe Mingione. Regularity results for electrorheological fluids: the stationary case. Comptes Rendus. Mathématique, Volume 334 (2002) no. 9, pp. 817-822. doi: 10.1016/S1631-073X(02)02337-3

Bibliographie
Cité par

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[2] E. Acerbi, G. Mingione, Regularity results for stationary electrorheological fluids, Arch. Rational Mech. Anal. (to appear)

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[6] P. Marcellini Everywhere regularity for a class of elliptic systems without growth conditions, Ann. Scuola Norm. Sup. Pisa, Volume 23 (1996), pp. 1-25

[7] K.R. Rajagopal; M. Růžička Mathematical modelling of electrorheological fluids, Contin. Mech. Thermodyn., Volume 13 (2001) no. 1, pp. 59-78

[8] M. Růžička Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Math., 1748, Springer, 2000

[9] M. Růžička Flow of shear dependent electrorheological fluids, C. R. Acad. Sci. Paris, Volume 329 (1999), pp. 393-398

[10] M. Růžička Flow of shear dependent electrorheological fluids: unsteady space periodic case (A. Sequeira, ed.), Appl. Nonlinear Anal., Plenum Press, 1999, pp. 485-504

[11] V.V. Zhikov Meyers-type estimates for solving the nonlinear Stokes system, Differential Equations, Volume 33 (1997), pp. 107-114

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