Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia
Copyright © 2009 Igor Pažanin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider a flow of incompressible Newtonian fluid through
a pipe with helical shape. We suppose that the flow is governed by the prescribed
pressure drop between pipe's ends. Such model has relevance to some important
engineering applications. Under small data assumption, we prove the existence and
uniqueness of the weak solution to the corresponding Navier-Stokes system with pressure
boundary condition. The proof is based on the contraction method.