Siberian Federal University

We consider a family of initial problems for the Navie–Stokes type equations generated by the de Rham complex in Rn [0; T], n > 2, with a positive time T over a scale weighted anisotropic H¨older spaces. As the weights control the order of zero at the infinity with respect to the space variables for vectors fields under the consideration, this actually leads to initial problems over a compact manifold with the singular conic point at the infinity. We prove that each problem from the family induces Fredholm open injective mappings on elements of the scales. At the step 1 of the complex we may apply the results to the classical Navier–Stokes equations for incompressible viscous fluid