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Measure-valued solutions and asymptotic behavior of a multipolar model of a boundary layer. (English) Zbl 0774.76008
The first chapter is devoted to the formulation of the problem for bipolar fluids. In the following two chapters, we deal with the global existence of weak solutions, regularity and smoothing effect. In the fourth chapter, the measure-valued solutions are defined and the behavior of the weak solutions under the vanishing higher viscosity is studied. The limits of strong viscous solutions exhibit the loss of regularity and satisfy equations of motion for monopolar fluids in the sense of regular measures. These conclusions are proved in chapter five. The sixth chapter concerns the uniqueness of weak solutions for bipolar fluids. In the last two chapters, we study the asymptotic behavior. The existence of the universal attractor with a finite Hausdorff dimension is proved.

##### MSC:
 76A05 Non-Newtonian fluids 76D10 Boundary-layer theory, separation and reattachment, higher-order effects 35Q35 PDEs in connection with fluid mechanics
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