TY - JOUR
T1 - Flexibility and Rigidity in Steady Fluid Motion
AU - Constantin, Peter
AU - Drivas, Theodore D.
AU - Ginsberg, Daniel
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature.
PY - 2021/7
Y1 - 2021/7
N2 - Flexibility and rigidity properties of steady (time-independent) solutions of the Euler, Boussinesq and Magnetohydrostatic equations are investigated. Specifically, certain Liouville-type theorems are established which show that suitable steady solutions with no stagnation points occupying a two-dimensional periodic channel, or axisymmetric solutions in (hollowed out) cylinder, must have certain structural symmetries. It is additionally shown that such solutions can be deformed to occupy domains which are themselves small perturbations of the base domain. As application of the general scheme, Arnol’d stable solutions are shown to be structurally stable.
AB - Flexibility and rigidity properties of steady (time-independent) solutions of the Euler, Boussinesq and Magnetohydrostatic equations are investigated. Specifically, certain Liouville-type theorems are established which show that suitable steady solutions with no stagnation points occupying a two-dimensional periodic channel, or axisymmetric solutions in (hollowed out) cylinder, must have certain structural symmetries. It is additionally shown that such solutions can be deformed to occupy domains which are themselves small perturbations of the base domain. As application of the general scheme, Arnol’d stable solutions are shown to be structurally stable.
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U2 - 10.1007/s00220-021-04048-4
DO - 10.1007/s00220-021-04048-4
M3 - Article
AN - SCOPUS:85102491281
SN - 0010-3616
VL - 385
SP - 521
EP - 563
JO - Communications In Mathematical Physics
JF - Communications In Mathematical Physics
IS - 1
ER -