Asymptotic Properties of Axis-Symmetric D-Solutions of the Navier-Stokes Equations

We consider asymptotic behavior of Leray's solution which expresses axis-symmetric incompressible Navier-Stokes flow past an axis-symmetric body. When the velocity at infinity is prescribed to be nonzero constant, Leray's solution is known to have optimum decay rate, which is in the class of physically reasonable solution. When the velocity at infinity is prescribed to be zero, the decay rate at infinity has been shown under certain restrictions such as smallness on the data. Here we find an explicit decay rate when the flow is axis-symmetric by decoupling the axial velocity and the horizontal velocities.