On the multivariate Burgers equation and the incompressible Navier-Stokes equation (Part I)

Abstract

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.