Existence of Weak Solutions for the Navier-stokes Equations with Initial Data in L P

@inproceedings{Caldern2009ExistenceOW,
title={Existence of Weak Solutions for the Navier-stokes Equations with Initial Data in L P},
author={C P Calder{\'o}n and P E Calderon},
year={2009}
}

The existence of weak solutions for the Navier-Stokes equations for the infinite cylinder with initial data in IY is considered in this paper. We study the case of initial data in IY(Rn), 2 < p < n, and n = 3,4. An existence theorem is proved covering these important cases and therefore, the "gap" between the Hopf-Leray theory (p = 2) and that of Fabes-Jones-Riviere (p > n) is bridged. The existence theorem gives a new method of constructing global solutions. The cases p = n are treated at the… CONTINUE READING