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.
$\endgroup$ 4What does it mean when one says that "the $L^2$-norm of $u$ is conserved"?
1 Answer
$\begingroup$It would be useful if you'd provide more context, as the precise meaning varies from case to case. In general, the term "conserved" occurs when you are studying something which is being changed, yet some property of the thing remains the same. We then say that this property is "conserved".
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 $u$.
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