Meaning of the arguments outside the operation? $(\nabla u \cdot \boldsymbol{n})(\boldsymbol{x},t)=0$

Question

What does it mean to write the arguments outside the functions, e.g. $(\nabla u \cdot \boldsymbol{n})(\boldsymbol{x},t)=0$? $\boldsymbol{n}$ is the unit outward normal vector to a surface.

Does it mean $\nabla u(\boldsymbol{x},t) \cdot \boldsymbol{n}=0$ or $\nabla u(\boldsymbol{x},t) \cdot \boldsymbol{n}(\boldsymbol{x},t)=0$ or maybe something else?

Answer 1

It's like $(fg) (x)$, which means $f(x) g(x)$. In your case it means

$$\big( (\nabla u) (x,t) \big) \cdot \big(\boldsymbol n(x,t) \big)$$

(with more paranthese added for more clarity).