A Note on the Pressure of Strong Solutions to the Stokes System in Bounded and Exterior Domains

We consider the Stokes problem in an exterior domain Ω ⊂ R n with an external force f ∈ L s ( 0 , T ; W k , r ( Ω ) ) ( k ∈ N , 1 < r < ∞ ) . In the present paper we show that in contrast to u the boundary regularity of the pressure can be improved according to the differentiability of f up to order k . In particular, this implies that the pressure is smooth with respect to x ∈ Ω if f is smooth with respect to x ∈ Ω .