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

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Abstract

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

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Authors and Affiliations

  1. Department of Mathematics, Chung-Ang University, Seoul, 156-756, Republic of Korea

    Jörg Wolf

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  1. Jörg Wolf
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Correspondence to Jörg Wolf.

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Communicated by G.P. Galdi.

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Wolf, J. A Note on the Pressure of Strong Solutions to the Stokes System in Bounded and Exterior Domains. J. Math. Fluid Mech. 20, 721–731 (2018). https://doi.org/10.1007/s00021-017-0341-6

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  • DOI: https://doi.org/10.1007/s00021-017-0341-6

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