Abstract
The most important impulse to the creation of the theory, is its ability to be a framework for the mathematical theory of compressible, heat conductive fluids. The theory provides proof of the existence of global (in time) solutions, what in spite of big efforts, the classical theory, based on linear Stoke’s stress-strain relation, does not make possible. The theory is compatible with principles of thermodynamics and with the principle of material frame indifference. The physical theory of multipolar fluids appeared in the paper by Nečas, Šilhavý [1] and follows the general ideas of Green, Rivlin [2], [3]. The mathematical theory is developed in a serie of papers by Nečas, Nečas, Šilhavý [4], [5], [6], Nečas, Novotný [7], Nečas [8], Málek, Nečas, Růžička [9], [10], Bellout, Bloom, Nečas [11], [12], where also limits to monopolar, in general non-newtonian fluids are studied.
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References
Nečas, J., Šilhavý, M.: Multipolar viscous fluids. Quarterly of Applied Mathematics XLIX (1991), 2, 247–266.
Green, A. E., Rivlin, R. S.: Simple force and stress multipoles. Arch. Rat. Mech. Anal. 16 (1964), 325–353.
Green, A.E., Rivlin, R. S.: Multipolar continuum mechanics. Arch. Rat. Mech. Anal. 17 (1964), 113–147.
Nečas, J., Novotný, A., Šilhavý, M.: Global solution to the ideal compressible multipolar heat conductive fluid. Comment. Math. Univ. Carol. 30 (1989), 3, 551–564.
Nečas, J., Novotný, A., Šilhavý, M.: Global solution to the compressible isothermal multipolar fluid. J. Math. Anal. and Appl. 161 (1991), 1, 223–241.
Nečas, J., Novotný, A., Šilhavý, M.: Global solution to the viscous compressible barotropic multipolar gas. Theoret. Comput. Fluid Dynamics 4 (1992), 1–11.
Nečas, J., Novotný, A.: Some quantitative properties of the viscous compressible heat conductive multipolar fluid. Commun in P. E. D. 16 (1991), (2 & 3), 197–220.
Nečas, J.: Theory of multipolar viscous fluids, the mathematics of finite elements and applications VII. In: MAFELAP 1990, Academic Press, 1991, 233-244.
Málek, J., Nečas, J., Růžička M.: Measure-valued solutions and asymptotic behavior of a multipolar model of a boundary layers. Czech Math. J. 42 (1992), 117, 549–576.
Málek, J., Nečas, J., Růžička, M.: On the non-newtonian incompressible fluids. Math. Models and Meth. in Appl. Sc., 3 (1993), 1, 35–63.
Bellout, H., Bloom, F., Nečas, J.: Uniqueness and stability to the initial boundary value problem for bipolar viscous fluids. SIAM J. Math. Anal. 24 (1993), 1, 26–45.
Bellout, H., Bloom, F., Nečas, J.: Phenomenological behavior of multipolar viscous fluids (to appear).
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© 1994 Springer Fachmedien Wiesbaden
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Nečas, J. (1994). Theory of Multipolar Fluids. In: Jentsch, L., Tröltzsch, F. (eds) Problems and Methods in Mathematical Physics. TEUBNER-TEXTE zur Mathematik. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-85161-1_10
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DOI: https://doi.org/10.1007/978-3-322-85161-1_10
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