The linear heat eqaution with potential $V\in L_{t,x}^{\frac{n+2}2}$ is well-posed for initial data in $L^p$ for any $p\in(1,\infty)$

Question

Consider the linear heat equation with potential $$u_t-\Delta u-V(x,t)u=0\qquad \text{in }\ \ \mathbb R^n\times[0,\infty),$$ where $V\in L_{t,x}^{\frac{n+2}2}$. Show that this equation is well-posed for initial data in $L^p$ for any $p\in(1,\infty)$.

This question comes from Hao Jia and Vladimir Sverak's paper, page 3739, where the authors claim the statement and indicate that it can be proved “by usual perturbation arguments”. I don't know what is the "usual arguments". So I'm asking here in which book or material I can learn this sort of thing.

Any help or useful reference will be appreciated.