Abstract The aim of the study is to analyse axisymmetric free vibration layered cylindrical shells filled with a quiescent fluid. fluid assumed be incompressible and inviscid. equations vibrations shell fluid, on longitudinal transverse displacement components are obtained using Love’s first approximation theory. solutions functions in separable form obtain system coupled differential terms fun...

appears for n = 3 in the pioneering Leray’s paper on the Navier-Stokes equations [2]. The constant factor on the right-hand side is sharp. Since one frequently deals with divergence-free fields in hydrodynamics, it is natural to ask whether this restriction can improve the constant in (1.1). We show in the present paper that this is the case indeed if n > 2 and the vector field u is axisymmetri...

We investigate an analytical treatment of bifurcations of families of resonant ‘thin’ tubes in axisymmetric galactic potentials. We verify that the most relevant bifurcations are due to the (1:1) resonance producing the ‘inclined’ orbits through two different mechanisms: from the disk orbit and from the ‘thin’ tube associated to the vertical oscillation. The closest resonances occurring after t...