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Stationary incompressible bipolar fluids. (English) Zbl 0816.76002

The title problem is approached using the notion of pseudomonotonicity. After introducing the physical foundation of the problem, the weak formulation is stated and justified in the second part. In the third chapter, the main results are collected, namely the existence of a solution to the weak problem is proven, and some regularity properties are shown.

MSC:

76A05 Non-Newtonian fluids
35Q35 PDEs in connection with fluid mechanics
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References:

[1] Nečas J.: Introduction to the Theory of Nonlinear Elliptic Equations. BSB B.G. Teubner Verlagsgesellschaft, Leipzig (1983). · Zbl 0526.35003
[2] Nečas J., Novotný A., Šilhavý M.: Global Solution to the Viscous Compressible Barotropic Fluid. to appear in J. Math. Anal. Appl.. · Zbl 0761.76006
[3] Nečas J., Novotný A., Šilhavý M.: Global Solution to the Ideal Compressible Heat Conductive Multipolar Fluid. Comment. Math. Univ. Carolinae 30,3 (1989), 551-564. · Zbl 0702.35205
[4] Nečas J., Novotný A., Šilhavý M.: Some Qualitative Properties of the Viscous Compressible Heat Conductive Multipolar Fluid. Commun. in Partial Differential Equation 16 (1991), no. 2&3, 197-220. · Zbl 0777.35061
[5] Nečas J., Šilhavý M.: Viscous Multipolar Fluids. to appear in Quarterly for Applied Mathematics. · Zbl 0732.76003
[6] Novotný A.: Viscous Multipolar Fluids. Thesis, Prague, 1990.
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