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Existence and uniqueness of steady flows of nonlinear bipolar viscous fluids in a cylinder

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  • The existence and uniqueness of solutions to the boundary-value problem for steady Poiseuille flow of an isothermal, incompressible, nonlinear bipolar viscous fluid in a cylinder of arbitrary cross-section is established. Continuous dependence of solutions, in an appropriate norm, is also established with respect to the constitutive parameters of the bipolar fluid model, as these parameters converge to zero, under the additional assumption that the cylinder has a circular cross-section.
    Mathematics Subject Classification: Primary: 76A05; Secondary: 35K52.


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