M. Bildhauer, M. Fuchs, X. Zhong, “On strong solutions of the differential equations modeling the steady flow of certain incompressible generalized Newtonian fluids”, Algebra i Analiz, 18:2 (2006), 1–23; St. Petersburg Math. J., 18:2 (2007), 183

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Algebra i Analiz, 2006, Volume 18, Issue 2, Pages 1–23 (Mi aa66)

This article is cited in 12 scientific papers (total in 12 papers)

Research Papers

On strong solutions of the differential equations modeling the steady flow of certain incompressible generalized Newtonian fluids

M. Bildhauer^a, M. Fuchs^a, X. Zhong^b

^a Department of Mathematics, Saarland University, Saarbrücken, Germany
^b Department of Mathematics and Statistics, University of Jyväskylä, Finland

Full-text PDF (226 kB) Citations (12)

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Abstract: A system of nonautonomous partial differential equations describing the steady flow of an incompressible fluid is considered. The existence of a strong solution of that system is proved under suitable assumptions on the data. In the 2D-case this solution turns out to be of class

C^{1, α}

$C^{1,\alpha}$ .

Keywords: generalized Newtonian fluids, anisotropic dissipative potentials, existence and regularity of solutions.

Received: 31.10.2005

English version:
St. Petersburg Mathematical Journal, 2007, Volume 18, Issue 2, Pages 183–199
DOI: https://doi.org/10.1090/S1061-0022-07-00948-X

Bibliographic databases:

Document Type: Article

MSC: 76M30, 76B03, 35Q35

Language: English

Citation: M. Bildhauer, M. Fuchs, X. Zhong, “On strong solutions of the differential equations modeling the steady flow of certain incompressible generalized Newtonian fluids”, Algebra i Analiz, 18:2 (2006), 1–23; St. Petersburg Math. J., 18:2 (2007), 183–199

Citation in format AMSBIB

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\jour Algebra i Analiz

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\vol 18

\issue 2

\pages 1--23

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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2244934}

\zmath{https://zbmath.org/?q=an:1129.35061}

\transl

\jour St. Petersburg Math. J.

\yr 2007

\vol 18

\issue 2

\pages 183--199

\crossref{https://doi.org/10.1090/S1061-0022-07-00948-X}

Linking options:

https://www.mathnet.ru/eng/aa66

https://www.mathnet.ru/eng/aa/v18/i2/p1

This publication is cited in the following 12 articles:

Moussa H., Rhoudaf M., Sabiki H., “Existence Results For a Perturbed Dirichlet Problem Without Sign Condition in Orlicz Spaces”, Ukr. Math. J., 72:4 (2020), 585–606
H. Moussa, M. Rhoudaf, H. Sabiki, “Existence results for a perturbed Dirichlet problem without sign condition in Orlicz spaces”, Ukr. Mat. Zhurn., 72:4 (2020), 509
Moussa H., Ortegon Gallego F., Rhoudaf M., “Capacity Solution to a Coupled System of Parabolic-Elliptic Equations in Orlicz-Sobolev Spaces”, NoDea-Nonlinear Differ. Equ. Appl., 25:2 (2018), 14
Bae H.-O., So H., Youn Y., “Interior Regularity to the Steady Incompressible Shear Thinning Fluids With Non-Standard Growth”, Netw. Heterog. Media, 13:3 (2018), 479–491
Moussa H., Rhoudaf M., Sabiki H., “Existence Results For Diffusion-Convection Equations of Nonlinear Unilateral Problems Defined in Orlicz-Sobolev Spaces”, Asian-Eur. J. Math., 11:6 (2018), 1850079
Bildhauer M., Fuchs M., Mueller J., “Existence and Regularity For Stationary Incompressible Flows With Dissipative Potentials of Linear Growth”, J. Math. Fluid Mech., 20:4 (2018), 1567–1587
Moussa H., Rhoudaf M., “Existence of Renormalized Solution of Nonlinear Elliptic Problems With Lower Order Term in Orlicz Spaces”, Ric. Mat., 66:2 (2017), 591–617
Berselli L.C., Breit D., Diening L., “Convergence analysis for a finite element approximation of a steady model for electrorheological fluids”, Numer. Math., 132:4 (2016), 657–689
Moussa H., Rhoudaf M., “Study of Some Non-linear Elliptic Problems with No Continuous Lower Order Terms in Orlicz Spaces”, Mediterr. J. Math., 13:6 (2016), 4867–4899
Fuchs M., “A note on non-uniformly elliptic Stokes-type systems in two variables”, J. Math. Fluid Mech., 12:2 (2010), 266–279
Beirão da Veiga H., “On the global regularity of shear thinning flows in smooth domains”, J. Math. Anal. Appl., 349:2 (2009), 335–360
Crispo F., Grisanti C.R., “On the $C^{1,\gamma}(\overline\Omega)\cap W^{2,2}(\Omega)$ regularity for a class of electro-rheological fluids”, J. Math. Anal. Appl., 356:1 (2009), 119–132

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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