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.