Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 93, pp. 1-14.

Title: Solutions to three-dimensional Navier-Stokes equations
       for incompressible fluids

Author: Jorma Jormakka (National Defence Univ., Helsinki, Finland)

Abstract:
 This article gives explicit solutions to the space-periodic
 Navier-Stokes problem with non-periodic pressure.
 These type of solutions are not unique and by using such solutions
 one can construct a periodic, smooth, divergence-free initial
 vector field allowing a space-periodic and time-bounded external
 force such that there exists a smooth solution to the
 3-dimensional Navier-Stokes equations for incompressible fluid
 with those initial conditions, but the solution cannot be continued
 to the whole space.

Submitted August 31, 2009. Published July 07, 2010.
Math Subject Classifications: 35Q30.
Key Words: Partial differential equations; Navier-Stokes equation;
           fluid dynamics.