what is the meaning of Galilei Inveriance ?

please help to explain it....

It's an expression of Newtons first law; i.e. the equivalence of inertial frames. This basically means that the equations of motion must be the same in all inertial frames.

If we have two inertial frames one at rest x and another moving at constant velocity c with respect to x, X say, then

X = x - ct

The velocity v measured in frame x is then V=v-c in frame X. The equations of motion in frame X is obtained from that in frame x by replacing x,v with X,V. This is Galilean invariance.

It's VERY basic physics.

the problem it's VERY BasiC PhysicS

thanks Tom

Hi,

Can you suggest some literature or book specially for Navier-Stoke equation.

Regards

It depends on your background and what you want to know. (I'm a mathematician and so the following are rather biased):

A good basic text is

Elementary fluid dynamics bt David Acheson (Oxford University Press)

An introduction to fluid dynamics by Paterson (Cambridge University Press)

is also a reasonable book. If you have a more physics based background then

An introduction to fluid dynamis by G.K. Batchelor (Cambridge University Press)

is probably a good place to start.

Hydrodynamics by Lamb (Cambridge/Dover?) is also worth a look (although it's pre-tensor analysis) as are

Theoretical hydrodynamics and Theoretical aerodynamics

both by Milne-Thompson and published by Dover.

For more rigorous discussion try

Applied analysis of the Navier-Stokes equations by Doering and Gibbon (Cambridge Unversity Press)

or, if you can find it,

The mathematical theory of incompressible viscous flow by O.A. Ladyzhenskaya

There's also a two volume set by Pierre-Louis Lions (Oxford University Press) but I haven't seen these (yet) and various books by Roger Temam.