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The monotonicity of the change in the first eigenvalue for a class of nonselfadjoint boundary value problems in the theory of hydrodynamical stability. (English. Russian original) Zbl 0579.76043
Transl., Ser. 2, Am. Math. Soc. 125, 33-43 (1985); translation from problems in mechanics and mathematical physics, Moskow 1976, 21-30 (1976).
Summary: An eigenvalue problem arising in the theory of hydrodynamic stability is considered. Conditions are obtained under which the least positive eigenvalue depends monotonically on the length of the interval. These conditions can be used in the problem of the stability of rotational Couette flow of a viscous incompressible fluid between two concentric cylinders, and in the problem of the occurrence of convection in a spherical layer of a self-gravitating fluid bounded by solid walls.
MSC:
76E05 Parallel shear flows in hydrodynamic stability
76E15 Absolute and convective instability and stability in hydrodynamic stability
76U05 General theory of rotating fluids
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