On Steady Flows of Quasi-Newtonian Fluids in Orlicz–Sobolev Spaces

Автор(и)

  • Farah Balaadich University of Sidi Mohamed Ben Abdallah, Faculty of Sciences Dhar El Mahraz, B.P. 1796 Atlas, Fez, Morocco
  • Elhoussine Azroul University of Sidi Mohamed Ben Abdallah, Faculty of Sciences Dhar El Mahraz, B.P. 1796 Atlas, Fez, Morocco

DOI:

https://doi.org/10.15407/mag17.03.263

Анотація

Стаття присвячена дослiдженню iснуванню слабких розв’язкiв для стацiонарних квазiньютонiвських течiй за допомогою наближень Гальоркiна i розв’язкiв у просторах мiр, а саме, мiр Янга, якi виявилися хорошим iнструментом для опису слабких розв’язкiв нашої задачi в просторах Орлича.

Mathematics Subject Classification: 35J65, 35Q35, 46E30

Ключові слова:

квазiньютонiвська рiдина, простори Орлича, слабка монотоннiсть, слабкий розв’язок, мiри Янга

Посилання

N. Arada and A. Sequeira, Existence results for steady flows of quasi-Newtonian fluids using weak monotonicity, J. Math. Fluid Mech. 7 (2005), S273–S288. https://doi.org/10.1007/s00021-005-0159-5

H. Attouch, G. Buttazzo and G. Michaille, Variational Analysis in Sobolev and BV Spaces, SIAM, Philadelphia, 2005. https://doi.org/10.1137/1.9780898718782

E. Azroul and F. Balaadich, Existence of weak solutions for quasilinear elliptic systems in Orlicz spaces, Appl. Anal. (2019), https://doi.org/10.1080/00036811. 2019.1680829. https://doi.org/10.1080/00036811.2019.1680829

E. Azroul and F. Balaadich, Quasilinear elliptic systems with nonstandard growth and weak monotonicity, Ricerche Mat. (2019), https://doi.org/10.1007/ s11587-019-00447-x. https://doi.org/10.1007/s11587-019-00447-x

E. Azroul and F. Balaadich, Young measure theory for unsteady problems in Orlicz– Sobolev spaces, Rend. Circ. Mat. Palermo Ser. 2, (2019), https://doi.org/10. 1007/s12215-019-00472-7. https://doi.org/10.1007/s12215-019-00472-7

E. Azroul and F. Balaadich, Strongly quasilinear parabolic systems in divergence form with weak monotonicity, Khayyam J. Math. 6 (2020), No. 1, 57–72.

E. Azroul and F. Balaadich, Quasilinear elliptic systems in perturbed form, Int. J. Nonlinear Anal. Appl. 10 (2019), No. 2, 255–266.

E. Azroul and F. Balaadich, A weak solution to quasilinear elliptic problems with perturbed gradient, Rend. Circ. Mat. Palermo (2) (2020), https://doi.org/10. 1007/s12215-020-00488-4. https://doi.org/10.1007/s12215-020-00488-4

F. Balaadich and E. Azroul, Existence and uniqueness results for quasilinear parabolic systems in Orlicz spaces, J. Dyn. Control Syst. (2019), https://doi. org/10.1007/s10883-019-09447-4. https://doi.org/10.1007/s10883-019-09447-4

J.M. Ball, A version of the fundamental theorem for Young measures, PDEs and continuum models of phase transitions, (1989), 207–215. https://doi.org/10.1007/BFb0024945

G. Dolzmann, N. Hungerühler, and S. Muller, Nonlinear elliptic systems with measure-valued right hand side, Math. Z. 226 (1997), 545–574. https://doi.org/10.1007/PL00004354

T. Donaldson, Inhomogeneous Orlicz–Sobolev spaces and nonlinear parabolic initialboundary value problems, J. Diff. Equat. 16 (1974), 201–256. https://doi.org/10.1016/0022-0396(74)90012-6

P. Gwiazda and A. Świerczewska-Gwiazda, On steady non-Newtonian fluids with growth conditions in generalized Orlicz spaces, Topol. Methods Nonlinear Anal. 32 (2008), No. 1, 103–113.

P. Gwiazda, P. Minakowski and A. Świerczewska-Gwiazda, On the anisotropic Orlicz spaces applied in the problems of continuum mechanics, Discrete Contin. Dyn. Syst. Ser. S 6 (2013), No. 5, 1291–1306. https://doi.org/10.3934/dcdss.2013.6.1291

N. Hungerühler, A refinement of Ball’s theorem on Young measures, N.Y. J. Math. 3 (1997), 48–53.

N. Hungerbühler, Quasilinear Elliptic Systems in Divergence Form with Weak Monotonicity, New York J. Math. 5 (1999), 83–90.

N. Hungerbühler, Young Measures and Nonlinear PDEs, Habilitationsschrift, ETH Zr̈ich, 2000.

M.A. Krasnosel’skiĭ and J.B. Rutickiĭ, Convex Functions and Orlicz Spaces, P. Noordhofi Ltd., Groningen, 1961.

A. Kufner, O. John, and S. Fucı́k, Function Spaces, Academia, Prague, 1977.

O.A. Ladyzhenskaya, Modification of the Navier–Stokes equations for the large velocity gradients, in: Boundary Value Problems of Mathematical Physics and Related Aspects of Function Theory II. Consultants Bureau, New York, 1968, 57–59.

O.A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, Gordon and Beach, New York, 1969.

R. Landes, On Galerkins method in the existence theory of quasilinear elliptic equations, J. Funct. Anal. 39 (1980), 123–148. https://doi.org/10.1016/0022-1236(80)90009-9

R. Landes, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod, Gauthier–Villars, Paris, 1969.

L. Nirenberg, Topics in Nonlinear Functional Analysis, Lecture Notes. Courant Institute, New York (1974).

M. Valadier,A course on Young measures, Workshop on Measure Theory and Real Analysis, (Grado, 1993). Rend. Istit. Mat. Univ. Trieste 26 (1994), 349–394.

A. Wroblewska, Steady flow of non-Newtonian fluids-monotonicity methods in generalized Orlicz spaces, Nonlinear Anal. 72 (2010) 4136–4147. https://doi.org/10.1016/j.na.2010.01.045

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Balaadich, F.; Azroul, E. On Steady Flows of Quasi-Newtonian Fluids in Orlicz–Sobolev Spaces. Журн. мат. фіз. анал. геом. 2021, 17, 263-279.

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