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We show the existence of solutions of the Navier-Stokes equations for which the Dirichlet norm, ||Vu(ί)||L2/Ωv, of the velocity is continuous as t = 0, while the normalized iΛnorm, l|p(0ll£2(QwΛ, of the pressure is not. This runs counter to the naive expectation that the relative orders of the spatial derivatives of u, p and ut should he the same in a priori estimates for the solutions as in the equations themselves.

A counterexample concerning the pressure in the Navier-Stokes equations, ast→ 0+

A counterexample concerning the pressure in the Navier-Stokes equations, ast→ 0⁺