On the fundamental solutions to Stokes equations

We study the behavior of solutions to the stationary Stokes equations near singular points. Employing the power series expansions of harmonic and biha rmonic functions, we have local power series expansions of solutions near s ingular points. Then we find the precise structures of homogeneous solution s near singular points which appear in local power series expansions. From the structures of the homogeneous solutions we characterize the fundamental solutions. Moreover, we study the asymptotic behavior of solutions to Stok es and Navier-Stokes equations under an assumption on directions of velocit ies. (C) 1999 Academic Press.