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We discuss the Navier-Stokes equations for an incompressible fluid wit a viscosity that is allowed to depend on the pressure. Ellipticity and the complementing condition of Agmon, Douglis and Nirenberg [l] are discussec It is found that the pressure dependence of viscosity leads to the possibilit of a change of type. It is shown that the Dirichlet initial-boundary valu problem is well posed as long as the equations do not change type
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Michael Renardy (1986) studied this question.
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