TY - JOUR
T1 - Hadamard variational formula for eigenvalues of the Stokes equations and its application
AU - Jimbo, Shuichi
AU - Kozono, Hideo
AU - Teramoto, Yoshiaki
AU - Ushikoshi, Erika
N1 - Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg.
PY - 2017/6/1
Y1 - 2017/6/1
N2 - Based on the explicit representation of the Hadamard variational formula [1] for eigenvalues of the Stokes equations, we investigate the geometry of the domain in R3. It turns out that if the first variation of some eigenvalue of the Stokes equations for all volume preserving perturbations vanishes, then the domain is necessarily diffeomorphic to the 2-dimensional torus T2.
AB - Based on the explicit representation of the Hadamard variational formula [1] for eigenvalues of the Stokes equations, we investigate the geometry of the domain in R3. It turns out that if the first variation of some eigenvalue of the Stokes equations for all volume preserving perturbations vanishes, then the domain is necessarily diffeomorphic to the 2-dimensional torus T2.
KW - 35Q10
UR - http://www.scopus.com/inward/record.url?scp=84963752050&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84963752050&partnerID=8YFLogxK
U2 - 10.1007/s00208-016-1410-5
DO - 10.1007/s00208-016-1410-5
M3 - Article
AN - SCOPUS:84963752050
SN - 0025-5831
VL - 368
SP - 877
EP - 884
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 1-2
ER -