What does the notation $D$ mean here?

Question

---

---

So what does the notation $D$ mean in the definition of relative entropy?

I try to explain the $D$ as $\nabla_{(\rho,u)}$, but it seems not right.

The article is "EXISTENCE AND UNIQUENESS OF GLOBAL STRONG SOLUTIONS FOR ONE-DIMENSIONAL COMPRESSIBLE NAVIER–STOKES EQUATIONS"

DOI. 10.1137/060658199

Answer 1

There is a clerical error. There should be a $\frac{1}{2}$

$D$ means $\nabla_{(\rho,m)}$