# What does “conserved” mean in mathematics?

Hope this is not a stupid "what is X" question.

I read a book from applied mathematics and I failed to find any reference for the concept "conserved". I am not sure if this is a mathematical jargon or if there is a definition for it.

What do people mean when he/she say that "the $L^2$-norm of u is conserved"?

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possible duplicate of the minimization of a functional from stochastic differential equations – PEV Apr 12 '11 at 22:35
Corrected. Thanks. – Jack Apr 12 '11 at 22:58
It means that the value is unchanged. To quote Wikipedia, "In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves." – Dave Radcliffe Apr 12 '11 at 23:17
It would be useful if you'd provide more context, but I'd guess that the is some transformation $t$ acting on $u$, in which case this means that the $L^2$-norm of $t(u)$ is the same as the $L^2$ norm of $u$. – Alex Becker Apr 12 '11 at 23:17
@Alex @Dave: I think both of those comments are reasonable answers to the question. May I convince you to post them as such? – Willie Wong Apr 12 '11 at 23:42

In your case, I'd guess that you have some transformation $t$ acting on $u$, in which case "the $L^2$-norm of $u$ is conserved" means that the $L^2$-norm of $t(u)$ is the same as the $L^2$-norm of $u$.