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

초록

We consider the Stokes problem in an exterior domain Omega subset of R(n )with an external force f is an element of L-s (0, T: W (k,r) (Omega)) (k is an element of N, 1 < r < infinity). 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 is an element of Omega if f is smooth with respect to x is an element of Omega.

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