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.

Résumé
Abstract

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].

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

@article{CRMATH_2002__334_9_817_0,
     author = {Emilio Acerbi and Giuseppe Mingione},
     title = {Regularity results for electrorheological fluids: the stationary case},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {817--822},
     publisher = {Elsevier},
     volume = {334},
     number = {9},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02337-3},
     language = {en},
}

TY  - JOUR
AU  - Emilio Acerbi
AU  - Giuseppe Mingione
TI  - Regularity results for electrorheological fluids: the stationary case
JO  - Comptes Rendus. Mathématique
PY  - 2002
SP  - 817
EP  - 822
VL  - 334
IS  - 9
PB  - Elsevier
DO  - 10.1016/S1631-073X(02)02337-3
LA  - en
ID  - CRMATH_2002__334_9_817_0
ER  -

%0 Journal Article
%A Emilio Acerbi
%A Giuseppe Mingione
%T Regularity results for electrorheological fluids: the stationary case
%J Comptes Rendus. Mathématique
%D 2002
%P 817-822
%V 334
%N 9
%I Elsevier
%R 10.1016/S1631-073X(02)02337-3
%G en
%F CRMATH_2002__334_9_817_0

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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02337-3/

Bibliographie
Cité par

[1] E. Acerbi; G. Mingione Regularity results for a class of functionals with nonstandard growth, Arch. Rational Mech. Anal., Volume 156 (2001) no. 2, pp. 121-140

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

[3] A. Coscia; G. Mingione Hölder continuity of the gradient of p(x)-harmonic mappings, C. R. Acad. Sci. Paris, Volume 328 (1999), pp. 363-368

[4] J. Malek; J. Nečas; M. Rokyta; M. Růžička Weak and Measure Valued Solutions to Evolution Partial Differential Equations, Appl. Math. Math. Comput., 13, Chapman and Hall, 1996

[5] P. Marcellini Regularity of minimizers of integrals of the calculus of variations with nonstandard growth conditions, Arch. Rational Mech. Anal., Volume 105 (1989), pp. 267-284

[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

Cité par Sources :

Commentaires - Politique