Bipolar barotropic non-newtonian compressible fluids
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 34 (2000) no. 5, p. 923-934
@article{M2AN_2000__34_5_923_0,
     author = {Matu\v S\r u-Ne\v casov\'a, \v S\'arka and Medvidov\'a-Luk\'a\v cov\'a, M\'aria},
     title = {Bipolar barotropic non-newtonian compressible fluids},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {34},
     number = {5},
     year = {2000},
     pages = {923-934},
     zbl = {0992.76010},
     mrnumber = {1837761},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2000__34_5_923_0}
}
MatuŠů-Nečasová, Šárka; Medvidová-Lukáčová, Mária. Bipolar barotropic non-newtonian compressible fluids. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 34 (2000) no. 5, pp. 923-934. http://www.numdam.org/item/M2AN_2000__34_5_923_0/

[1] C. Amrouche and D. Cioranescu, On a class of fluids of grade 3, Laboratoire d'analyse numérique de l'université Pierre et Marie Curie, rapport 88006 (1988). | Zbl 0887.76007

[2] C. Amrouche, Sur une classe de fluides non newtoniens : les solutions aqueuses de polymère, Quart. Appl. Math. L(4) (1992) 779-791. | MR 1193666 | Zbl 0765.76002

[3] H. Bellout, F. Bloom and J. Nečas, Young measure-valued solutions for non-Newtonian incompressible fluids. Commun Partial Differential Equations 19 (1994) 1763-1803. | MR 1301173 | Zbl 0840.35079

[4] Beirão Da Veiga, An Lp - theory for the n-dimensional stationary compressible Navier-Stokes equations and the incompressible limit for compressible fluids. The equilibrium solutions Comm. Math. Phys. 109 (1987) 229-248. | MR 880415 | Zbl 0621.76074

[5] D. Cioranescu and E.H. Quazar, Existence and uniqueness for fluids of second grade Collège de France Seminars, Pitman Res Notes Math. Ser. 109 (1984) 178-197. | MR 772241 | Zbl 0577.76012

[6] E. Feireisl and H. Petzeltová, On the steady state solutions to the Navier-Stokes equations of compressible flow. Manuscripta Math. 97 (1998) 109-116. | MR 1642646 | Zbl 0910.35097

[7] E. Feireisl and H. Petzeltová, The zero - velocity limit solutions of the Navier-Stokes equations of compressible fluid revisited, in Proc. of Navier-Stokes equations and the Related Problem, (1999) | MR 1896932 | Zbl 1011.35102

[8] G.P. Galdi, Mathematical theory of second grade fluids, Stability and Wave Propagation in Fluids, G.P. Galdi Ed., CISM Course and Lectures 344, Springer, New York (1995) 66-103. | MR 1414954 | Zbl 0828.76006

[9] G.P. Galdi and A. Sequeira, Further existence results for classical solutions of the equations of a second grade fluid. Arch. Ration. Mech. Anal. 28 (1994) 297-321. | MR 1308855 | Zbl 0833.76005

[10] D.D. Joseph, Fluid Dynamics of Viscoelastic Liquids. Springer Verlag, New York (1990). | MR 1051193 | Zbl 0698.76002

[11] J. Málek, J. Nečas, M. Rokyta and R. Růžička, Weak and Measure-valued solutions to evolutionary partial differential equations. Chapman and Hall (1996). | Zbl 0851.35002

[12] A.E. Mamontov, Global solvability of the multidimensional Navier-Stokes equations of a compressible fluid with nonlinear viscosity. I Siberian Math. J. 40 (1999) 351-362. | MR 1698313 | Zbl 0938.35121

[13] A. E. Mamontov, Global solvability of the multidimensional Navier-Stokes equations of a compressible fluid with nonlinear viscosity II. Siberian Math. J. 40 (1999) 541-555 | MR 1709015 | Zbl 0928.35119

[14] Š Matušů-Nečasová and M. Medvid'Ová, Bipolar barotropic nonnewtonian fluid. Comment. Math. Univ. Carolin 35 (1994) 467-483. | MR 1307274 | Zbl 0809.76001

[15] Š. Matušů-Nečasová, A. Sequeira and J.H. Videman, Existence of Classical solutions for compressible viscoelastic fluids of Oldroyd type past an obstacle. Math. Methods Appl. Sci. 22 (1999) 449-460. | MR 1679127 | Zbl 0916.76004

[16] Š. Matušů-Nečasová and M. Medvid'Ová-Lukáčová, Bipolar Isothermal non-Newtonian compressible fluids. J. Math. Anal. Appl. 225 (1998) 168-192. | MR 1639232 | Zbl 0951.76004

[17] J. Nečas and M. Šilhavý, Multipolar viscous fluids. Quart. Appl. Math. XLIX (1991) 247-266 | MR 1106391 | Zbl 0732.76003

[18] J. Nečas, A. Novotný and M. Šilhavý, Global solutions to the viscous compressible barotropic multipolar gas. Theoret Comp. Fluid Dynamics 4 (1992) 1-11. | Zbl 0761.76006

[19] J. Nečas, Theory of multipolar viscous fluids, in The Mathematics of Finite Elements and Applications VII MAFELAP 1990, J.R. Whitemann Ed., Academic Press, New York (1991) 233-244. | MR 1132501 | Zbl 0815.76009

[20] J. Neustupa, A semigroup generated by the linearized Navier-Stokes equations for compressible fluid and its uniform growth bound in Hölder spaces, in Proc. of the International Conference on the Navier-Stokes equations, Theory and Numerical Methods, Varenna, June 1997, R. Salvi Ed, Pitman Res. Notes Math. Ser. 388 (1998) 86-100. | MR 1773588 | Zbl 0954.35130

[21] J. Neustupa, The global existence of solutions to the equations of motion of a viscous gas with an artificial viscosity. Math. Methods. Appl. Sci. 14 (1991) 93-119. | MR 1091171 | Zbl 0724.76073

[22] J.G. Oldroyd, On the formulation of rheological equations of state. Proc. Roy. Soc. London A200 (1950) 523-541. | MR 35192 | Zbl 1157.76305 | Zbl pre05542443

[23] K.R. Rajagopal, Mechanics of non-Newtonian fluids, in Recent Developments in Theoretical Fluid Mechanics Series 291, Longman Scientific & Technical Reports (1993). | MR 1268237 | Zbl 0818.76003

[24] M. Renardy, W.J. Hrusa and J.A. Nohel, Mathematical problems in Viscoelasticity, Longman, New York (1987). | MR 919738 | Zbl 0719.73013

[25] R. Salvi and I. Straškraba, Global existence for viscous compressible fluids and their behaviour as t → ∞. J. Faculty Sci. Univ. Tokyo, Sect. I, A40 (1993) 17-51. | MR 1217657 | Zbl 0785.35074

[26] W.R. Schowalter, Mechanics of Non-Newtonian Fluids. Pergamon Press, New York (1978).

[27] M.H. Sy, Contributions à l'étude mathématique des problèmes issus de la mécanique des fluides viscoélastiques. Lois de comportement de type intégral ou différentiel. Thèse d'université de Paris-Sud, Orsay (1996).

[28] C. Truesdell and W. Noll, The Nonlinear Field Theories of Mechanics, 2nd edn. Springer, Berlin (1992). | MR 1215940 | Zbl 0779.73004