  In the presence of a certain class of functions we show that there exists a
smooth solution to Navier-Stokes equation. This solution entertains the
property of being nonconvective. We introduce a definition for any possible
solution to the problem with minimum assumptions on the existence and the
regularity of such solution. Then we prove that the proposed class of functions
represents the unique solution to the problem and consequently we conclude that
there exists no convective solutions to the problem in the sense of the given
definition.
