  We provide a constructive global existence proof for the multivariate viscous
Burgers equation system defined on the whole space or on a domain isomorphic to
the n-torus and with time horizon up to infinity and C^{\infty}- data
(satisfying some growth conditions if the problem is posed on the whole space).
The proof is by a time discretized semiexplicit perturbative expansion in
transformed coordinates where the convergence is guaranteed by certain a priori
estimates. The scheme is useful in order to define computation for related
equation systems of fluid dynamics.
