Sergey E. Mikhailov
Brunel University London, UK

We consider the evolution (non-stationary) anisotropic Navier-Stokes equations with variable space-periodic viscosity coefficients in $\mathbb R^n$. Employing the Galerkin algorithm, we prove the existence of a global weak spatially-periodic solution for the Navier-Stokes system in a periodic Sobolev space. The solution uniqueness and regularity results are also discussed.