Can anyone please address me on a reference where I can find the following interpolation result (it is stated on many places as a standard one, but without a clear reference).
Let $\Omega \subset\subset R^d$ and $T>0$. If $u\in H^1([0,T];H^{-1}(\Omega))$ and $u\in L^2([0,T];H^{1}(\Omega))$ then $u \in H^s([0,T];H^{1-s}(\Omega))$, $0<s<1$.
I am so sorry if the question is trivial and I am very grateful for any input.