ABSTRACT
Let be a Riemannian n-dimensional smooth closed manifold,
,
be smooth vector bundles over
and
be an elliptic differential complex of linear first order operators. We consider the operator equations, induced by the Navier-Stokes type equations associated with
on the scale of anisotropic Hölder spaces over the layer
with finite time T>0. Using the properties of the differentials
and parabolic operators over this scale of spaces, we reduce the equations to a nonlinear Fredholm operator equation of the form
, where K is a compact continuous operator. It appears that the Fréchet derivative
is continuously invertible at every point of each Banach space under consideration and the map
is open and injective in the space.
AMS Subject Classifications:
Acknowledgements
We thank Prof. N. Tarkhanov for an essential help in the preparation of Section 4.
Disclosure statement
No potential conflict of interest was reported by the author(s).