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We show the existence of (a class of) weak solutions to the three-dimensionalstationary incompressible inhomogeneous Navier--Stokes equations withdensity-dependent viscosity coefficient in the axially symmetric case. Furthersymmetric solutions in cylindrical coordinates, spherical coordinates andCartesian coordinates are also discussed.

Three-dimensional stationary incompressible inhomogeneous Navier-Stokes equation in the axially symmetric case