Regularity results for electrorheological fluids: the stationary case
[Résultats de régularité pour les fluides électrorhéologiques : le cas stationnaire]
Comptes Rendus. Mathématique, Tome 334 (2002) no. 9, pp. 817-822.

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].

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DOI : 10.1016/S1631-073X(02)02337-3
Acerbi, Emilio 1 ; Mingione, Giuseppe 1

1 Dipartimento di Matematica, Via D'Azeglio, 85, 43100 Parma, Italie
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Acerbi, Emilio; Mingione, Giuseppe. Regularity results for electrorheological fluids: the stationary case. Comptes Rendus. Mathématique, Tome 334 (2002) no. 9, pp. 817-822. doi : 10.1016/S1631-073X(02)02337-3. http://www.numdam.org/articles/10.1016/S1631-073X(02)02337-3/

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

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

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

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

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

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

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

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

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