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 biharmonic functions, we have local power series expansions of solutions near singular points. Then we find the precise structures of homogeneous solutions 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 Stokes and Navier–Stokes equations under an assumption on directions of velocities.