A COUNTEREXAMPLE CONCERNING THE PRESSURE IN THE NAVIER-STOKES EQUATIONS, AS T-]0+

We show the existence of solutions of the Navier-Stokes equations for which the Dirichlet norm, \\delu(t)\\L2(OMEGA), of the velocity is con tinuous as t = 0, while the normalized L2-norm, \\p(t)\\L2(OMEGA)/R, o f the pressure is not. This runs counter to the naive expectation that the relative orders of the spatial derivatives of u, p and u(t) shoul d be the same in a priori estimates for the solutions as in the equati ons themselves.