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Bipolar Isothermal Non-Newtonian Compressible Fluids

by Necasova, S.M. , Lukácová-Medvidová, M.

Series: 1997-07, Preprints

76N10 Existence, uniqueness, and regularity theory
76A05 ~Non-Newtonian fluids
35Q35 PDEs in connection with fluid mechanics

existence and uniqueness of a solution to isothermal non-Newtonian bipolarfluid is proved. We consider a special case, where the stress tensor is expressedin the form of potentials depending on e ij and ( @e ij@xk ). The second part is devotedto the problem of the stability of the rest state. It is proved that the perturbationsof velocity and density tend to zero in appropriate norms along a chosen timesequence. Moreover we obtain the asymptotic stability of the rest state under theassumption of the regularity of the potential forces.

non-Newtonian compressible fluids, global existence, uniqueness,asymptotic stability, rest state