Doubt about 0-norm in Majda Bertozzi

Question

I'm studyind Majda Bertozzi book about vorticity and incompressible flow, and I don't know what's the 0 norm which appears in it. Thanks a lot!

Answer 1

As the first line of p. 89 says, $\|\cdot\|_0$ is the $L^2$ norm on $\mathbb{R}^N$. The $0$ makes sense when you check out p. 97, where this is generalised to Sobolev spaces of functions having derivatives up to order $m$ that are in $L^2$. $L^2$ is then the case $m=0$.