MathOverflow

I am looking for a reference which discusses the following technique of "formal" Lie integration:
Start with a Lie algebra $\mathfrak{g}$.
Take its universal enveloping algebra, $U(\mathfrak{g})$. This is a Hopf algebra with comultiplication $\Delta x=x\otimes1+1\otimes x$....

Let $p\in [1,\infty]$, and $\Omega\subset\mathbb{R}^N$ a bounded, open and connected set. If $u\in W^{1,p}((0,T);L^{p}(\Omega))$ and $f:\Omega\times\mathbb{R}\to \mathbb{R},\ f=f(x,s)$ be a $C^1$ function that is also globally Lipschitz.
Denote $v(t,x)=f(x,u(t,x))$....

Say that a group $G$ is full iff there is a set $X$ such that $G\cong S_X$. Prima facie, fullness is a $\Sigma^1_2$ condition. At MSE I sketched a (hopefully correct!) argument that there is no $\Pi^1_1$ definition of fullness which works in all $\mathsf...

I've been doing some low-level research on my free time. Just as a clarification, I hold a degree in pure mathematics but didn't pursue a phd. I don't have cranky aspirations of proving RH.
My way of going about this research is
Writing a lot by hand: questions to myself (why should this be true? is this inequality strong enough for what I need?...), some case-by-case computations, drafts of potential strategies, applying known methods with some modifications appropriate to...