关于稳定性的基本概念介绍（二）。

ustcsunl

LBSALE[1]LBSALE定常：steady
稳态：stationary
稳定：stable
The concept of steady means a field does not change with time.
An alternative concept "equilibrium", more mathematically, is
also refered to this state. Both conceptes are used for the
time-independent solutions of a time-dependent ODE/PDE
(ordinary/partial differential equations).
The concept of stationary, which is often used in turbulent
flows,  means statistically steady. It contains two facts:
(1) a stationary field is time-dependent, comparing with that
of the steady field, (2)The statistic of the filed (e.g. time-
mean of the field) is time-independent or steady.   
An intresting discussion about steady / stationary is recommended,
where coolboy gave a very nice explanation:
http://forum.cfluid.com/cgi-bin/LB5000/topic.cgi?forum=18&topic=508&start=0&show=0&man=
The concept of stability means whether the solution (more specificly,
stead solution) changes a lot as some perturbations are imposed. It
is original from the investigation of some mechanics problems. However,
the concept of stability and the correspondign theory had not been
mathematically estabilished untill Lyaponov published his famous Ph.D
thesis.
Physically, the stability is one the important problems in the
research of fluid dynamics. At least one-third of the papers in the
leading journals (e.g. JFM) are dealing with all kinds of instability
in the fluid dynamics. Often, the stability means the physics or
mechanisms in fluid dynamics.
Numerically, the stability of the numerical method is one of the
fundmental problems for the applications. The analysis or discussion
of the stability of scheme is always required in the top journals
(e.g. JCP).

jollage

用stability去发jfm是很好发。请问有Lyaponov的phd thesis吗？谢谢。