RESUMEN

Let ug  represent the velocity of a Bingham fluid in a bounded domain Ω of R², with initial value uº, and plasticity threshold g. In [5] it was shown that if g is large enough (say g ≥ gc) ug  becomes zero after some time. Moreover, [7] computed gc for the specific stationary case of a cylindrical pipe of section Ω, when the exterior forces are constant.

Our purpose is threefold: a) we show that ׀ ug ׀ (the L² (Ω) – energy of the fluid) is a decreasing function of g, proving thus a conjecture stated in [4] and verified numerically in [1]. b) we show that Bingham fluids have backward uniqueness properties before they (eventually) become zero. c) we strengthen some know results, thanks to the ones proven in a), b).

RESUMEN

It is shown that, given a Hilbert space of arbitrary dimension, there exists a quasinilpotent operator Q_u whose similarity orbit is norm-dense in the closure of the set of all nilpotent operators. Furthermore, a similar result holds for the compact operators and some other (but not for all) closed bilateral ideals of operators.