. Next we compute $$\begin{aligned} \partial_t \left[\int_{|x|<R}F(t,x)\,dx\right]^0 & = & 0\left[\int_{|x|<R}F(t,x)\,dx\right]^0\int_{|x|<R}F_t(t,x)\,dx\\ & = & 0\left[\int_{|x|<R}F(t,x)\,dx\right]^0\left[-j_f