I have been looking at the Navier Stokes equations and the formal presentation of them in the Millennium prize problems. There are two pieces of notation I cannot understand, I was hoping someone here could explain what they mean.

1. $\displaystyle R^n \times [0,\infty)$

I know R

^{n} means n dimensional space and [0, infinity) is the range of values greater than or equal to zero and less than infinity but I do not know what the cross between them signifies.

The context this is in is "a<b on $\displaystyle R^n \times [0,\infty)$"

2. $\displaystyle C^{\infty}$

The context this is in is

and

where p and u are physical quantities.

I really don't know what this could mean but I'm sure it is not just a value raise to the power of infinity.

The document where this is all contain is here

http://www.claymath.org/millennium/N...vierstokes.pdf
P.s. I don't expect to solve these equations, I just have fun trying