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The resolvent problem for the stokes system in exterior domains: An elementary approach
Author(s) -
Deuring Paul
Publication year - 1990
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670130406
Subject(s) - mathematics , resolvent , bounded function , domain (mathematical analysis) , semigroup , analytic semigroup , mathematical analysis , boundary (topology) , dirichlet problem , dirichlet boundary condition , representation (politics) , boundary value problem , integral equation , operator (biology) , pure mathematics , biochemistry , chemistry , repressor , politics , political science , transcription factor , law , gene
We consider the Stokes system with resolvent parameter in an exterior domain:under Dirichlet boundary conditions. Here Ω is a bounded domain with C 2 boundary, and [λϵℂ\] − [∞, 0], ν >0. Using the method of integral equations, we are able to construct solutions ( u , π) in L p spaces. Our approach yields an integral representation of these solutions. By evaluating the corresponding integrals, we obtain L p estimates that imply in particular that the Stokes operator on exterior domains generates an analytic semigroup in L p .