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

John Heywood, Owen Walsh
1994 Pacific Journal of Mathematics  
We show the existence of solutions of the Navier-Stokes equations for which the Dirichlet norm, ||Vu(ί)|| L 2/ Ω v, of the velocity is continuous as t = 0, while the normalized iΛnorm, l|p(0ll£2 (Q w Λ , of 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 should he the same in a priori estimates for the solutions as in the equations themselves.
doi:10.2140/pjm.1994.164.351 fatcat:jnpuf5327velbh63tvdw3adbru