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Keywords:
barotropic nonnewtonian fluid; bipolar fluid; existence; uniqueness; weak solution
barotropic nonnewtonian fluid; bipolar fluid; existence; uniqueness; weak solution
Summary:
The paper describes the special situation of barotropic nonnewtonian fluid, where stress tensor can be written in the form of potentials which depend on $e_{ij}$ and $(\frac {\partial e_{ij}}{\partial x_k})$. For this case, we prove the existence and uniqueness of weak solution.
References:
[1] Adams R.A.: Sobolev spaces. Academic Press, New York, San Francisco, London, 1975. MR 0450957
[2] Nečas J., Šilhavý M.: Multipolar viscous fluids. Quart. of Appl. Math. XLIX (1991), 247-266. MR 1106391
[3] Nečas J., Novotný A., Šilhavý M.: Global solutions to the compressible isothermal multipolar fluid. J. Math. Anal. Appl. (1991). MR 1135273
[4] Nečas J., Novotný A., Šilhavý M.: Global solutions to the viscous compressible barotropic multipolar gas. Theoret. Comp. Fluid Dynamics 4 (1992).
[5] Nečas J., Novotný A.: Some qualitative properties of the viscous compressible heat conductive multipolar fluid. Commun. in Part. Dif. Eq. 16 (1991). MR 1104099
[6] Lions J.J.: Quelques méthodes de résolution des problèmes aux limites nonlinéaires, Dunod, Paris, 1969.
[7] Kufner A., John O., Fučík S.: Functional Spaces. Academia Prague, 1977.
[8] Málek J., Nečas J., Růžička: Measure valued solutions to nonnewtonian incompressible fluids in bounded domains. to appear.
[9] Nečas J.: Les méthodes directes en théorie des équations elliptiques. Prague, 1967. MR 0227584
[10] Matušů-Nečasová Š.: Global solution to the isothermal compressible bipolar fluid in a finite channel with nonzero input and output. Applications of Mathematics 36 (1991), 46-71. MR 1093482
[11] Nečas J.: Theory of multipolar viscous fluids. The Mathematics of Finite Elements and Applications VII (1991), 233-244. MR 1132501
[12] Bellout H., Bloom R., Nečas J.: Phenomenical behaviour of multipolar viscous fluid. to appear in the Quaterly Appl. Math.
[13] Nečas J.: Sur les normes équivalentes dans $ W_p^k(Ømega)$ et sur la coercivité des formes formellement positives. Les presses de l'Université de Montréal, 1966.
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