Existence of Weak Solutions for the Navier-Stokes Equations with Initial Data in L p

Calixto P. Calderon
1990 Transactions of the American Mathematical Society  
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
more » ... are treated at the end of the paper.
doi:10.2307/2001234 fatcat:2edvs3ik75g4vfgw6hylhhnoci