S.G. Kazantsev
Orthogonal polynomial basis 
in the space of vector functions ${\bf H}_0^1$ 
and
   Stokes system in a ball
 
 Abstract. 
 In the homogeneous Sobolev space of vector 
 functions
 ${\bf H}_0^1({\mathbb B}^3)$
 orthogonal
polynomial
 basis is constructed.
 Some of this vector functions,
 in particular,  are vector potentials 
 for solenoidal  fields from the  
 basis of the space  $ {\bf L}_2({\mathbb B}^3)$.
 As the result, the Dirichlet boundary  
 value problem for the stationary Stokes 
 system in a ball is solved. 
 The solution is presented as  a series on 
 the constructed polynomial basis 
 vector functions.

 Keywords:
 Vector spherical harmonics, vector functions,
 potential field, solenoidal field, 
 polynomial vector functions, 
 Sobolev space, orthogonal basis,Stokes problem