Abstract
This paper treats the Stokes problem in exterior Lipschitz-continuous domains of ℝ2 and ℝ3. Using the weighted Sobolev spaces of Hanouzet (in ℝ3) and Giroire (in ℝ2), we establish the inf-sup condition between the velocity and pressure spaces. This fundamental result shows that the variational Stokes problem is well-posed in those spaces. In the last paragraph, we obtain additional regularity of the solution when the data are smoother.
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Girault, V., Sequeira, A. A well-posed problem for the exterior Stokes equations in two and three dimensions. Arch. Rational Mech. Anal. 114, 313–333 (1991). https://doi.org/10.1007/BF00376137
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DOI: https://doi.org/10.1007/BF00376137