Abstract
Existence of a conjugate point in the incompressible Euler flow on a sphere and an ellipsoid is considered. Misiołek (1996) formulated a differential-geometric criterion (we call the M-criterion) for the existence of a conjugate point in a fluid flow. In this paper, it is shown that no zonal flow (stationary Euler flow) satisfies the M-criterion if the background manifold is a sphere, on the other hand, there are zonal flows satisfy the M-criterion if the background manifold is an ellipsoid (even it is sufficiently close to the sphere). The conjugate point is created by the fully nonlinear effect of the inviscid fluid flow with differential geometric mechanism.
Funding Statement
Research of the first author was partially supported by Foundation of Research Fellows, The Mathematical Society of Japan. Research of the second author was partially supported by Grant-in-Aid for Young Scientists A (17H04825), Grant-in-Aid for Scientific Research B (15H03621, 17H02860, 18H01136 and 18H01135).
Citation
Taito TAUCHI. Tsuyoshi YONEDA. "Existence of a conjugate point in the incompressible Euler flow on an ellipsoid." J. Math. Soc. Japan 74 (2) 629 - 653, April, 2022. https://doi.org/10.2969/jmsj/83868386
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