(−1)-homogeneous axisymmetric no-swirl solutions of three dimensional incompressible stationary Navier-Stokes equations which are smooth on the unit sphere minus the north and south poles have been classified. In this paper we study the vanishing viscosity limit of sequences of these solutions. As the viscosity tends to zero, some sequences of solutions Cloc m converge to solutions of Euler equations on the sphere minus the poles, while for other sequences of solutions, transition layer behaviors occur. For every latitude circle, there are sequences which Cloc m converge respectively to different solutions of the Euler equations on the spherical caps above and below the latitude circle. We give detailed analysis of these convergence and transition layer behaviors.
All Science Journal Classification (ASJC) codes
- Homogeneous axisymmetric no-swirl solutions
- Stationary Navier-Stokes equations
- Vanishing viscosity limit