10. Fill $[1, \sqrt{3}]$. Reason: First, find the domain of the given function $y=\arcsin \left(2-x^{2}\right)$: $-1 \leqslant 2-x^{2} \leqslant 1$, which means $1 \leqslant x^{2} \leqslant 3$, or equivalently $-\sqrt{3} \leqslant x \leqslant-1$ or $1 \leqslant x \leqslant \sqrt{3}$. Since $\arcsin x$ is an increasing function, when $2-x^{2}$ decreases, $\arcsin \left(2-x^{2}\right)$ also decreases. The function $2-x^{2}$ is decreasing on the interval $[0,+\infty)$, and $[1, \sqrt{3}] \subset[0,+\infty)$, so the required decreasing interval is $[1, \sqrt{3}]$.
10. The monotonic decreasing interval of the function $y=\arcsin \left(2-x^{2}\right)$ is