Does Sobolev spaces $H^s$ continuously embed into $L^2$? It seems like this is the case from this post
https://en.wikipedia.org/wiki/Rigged_Hilbert_space
where can i find a list of continuous sobolev embedding? The only thing I can find is Sobolev embedding theorem, which does cover what I have written here.
Yes, $H^s$ embeds continuously to $L^2=H^0$ for any $s\geq0$. (And it fails for all $s<0$. In fact, $H^s$ embeds continuously to $H^r$ whenever $r\leq s$.)
The norm on $H^s(\mathbb R^n)$ is (up to a constant that you are free to choose) $$ \|f\|_{H^s} = \|w(\cdot)^s\hat f(\cdot)\|_{L^2}, $$ where $\hat f$ is the Fourier transform of $f$ and $w(x)=(1+|x|^2)^{1/2}$. Since $w(s)^s\geq1$, you have $\|f\|_{H^s}\geq\|f\|_{L^2}$.