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The Stokes equations in layer domains on spaces of bounded and integrable functions
Author(s) -
Below Lorenz,
Bolkart Martin
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201500198
Subject(s) - mathematics , bounded function , resolvent , domain (mathematical analysis) , integrable system , mathematical analysis , semigroup , linear subspace , solenoidal vector field , pure mathematics , dimension (graph theory) , geometry , vector field
The Stokes equations in a layer domain are investigated. For the case of a two‐dimensional layer it is shown by resolvent estimates that there exists a semigroup of angle π / 2 on solenoidal subspaces of L ∞ and L 1 . Furthermore, the stationary problem for dimension two is solvable in these spaces. It is also shown that both results cannot be extended to three and higher dimensions in the same setting.