97-07
Bipolar Isothermal Non-Newtonian Compressible Fluids
by S.M. Necasova (Prag); M Lukácová-Medvidová (Magdeburg)
Preprint series: 97-07, Preprints
- MSC:
- 76N10 Compressible fluids, general, See also {35Q30}
- 76A05 Non-Newtonian fluids
- 35Q35 Other equations arising in fluid mechanics
Abstract: The existence and uniqueness of a solution to isothermal non-Newtonian bipolar fluid is proved. We consider a special case, where the stress tensor is expressed in the form of potentials depending on e ij and ( @e ij @xk ). The second part is devoted to the problem of the stability of the rest state. It is proved that the perturbations of velocity and density tend to zero in appropriate norms along a chosen time sequence. Moreover we obtain the asymptotic stability of the rest state under the assumption of the regularity of the potential forces.
Keywords: non-Newtonian compressible fluids, global existence, uniqueness,asymptotic stability, rest state