In this paper.we make some comparisons between the solutions for Narier-Stokes equation and those.for heat conduction equation.In his study of Navier-Stokes equation.Professor J.Leray.a French mathematician and authority on partial differential equation,starting from heat conduction equation,obtained some results of properly posed of certain initial boundary value problems of Navier-Stokes equation.Professor R.Temam of University de Paris XI and other experts in this field also brought up the possibility of comparing these two classes of equations.This paper attempts to describe and provethe.fundamental difference between these two.