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On the principal eigenvalue of the Stokes operator in cylindrical domains
Author(s) -
Karpiński Mikołaj,
Nowakowski Bernard,
Ströhmer Gerhard
Publication year - 2018
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201700366
Subject(s) - eigenvalues and eigenvectors , operator (biology) , mathematics , mathematical analysis , laplace operator , dirichlet boundary condition , boundary value problem , boundary (topology) , physics , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene
We consider the Stokes operator in periodic, three dimensional cylinders supplemented with four types of the boundary conditions: the zero Dirichlet b.c., the Navier b.c., the slip b.c. and the generalized impermeability b.c. We analyze the relation between the principal eigenvalue of the Stokes operator and the diameter of the base of the cylinder. Since the direct computation of the eigenvalues for the Stokes system is very difficult, we examine the vector‐valued Laplacian and then draw some conclusions for the Stokes operator.