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A well-posed problem for the exterior Stokes equations in two and three dimensions

โœ Scribed by Vivette Girault; Adelia Sequeira

Publisher
Springer
Year
1991
Tongue
English
Weight
832 KB
Volume
114
Category
Article
ISSN
0003-9527

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โœฆ Synopsis

This paper treats the Stokes problem in exterior Lipschitz-continuous domains of R 2 and R 3. Using the weighted Sobolev spaces of HANOUZEr (in R 3) and GIRoIP, E (in t~2), 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.

๐Ÿ“œ SIMILAR VOLUMES

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## Abstract The Dirichlet problems for the Stokes resolvent equations are studied from the point of view of the theory of hydrodynamic potentials. Existence and uniqueness results as well as boundary integral representations of classical solutions are given for domains having compact but not connec