Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
I have learned that there are plenty of work on the weak solution or strong solution for such system. However, there seems to be seldom discussions on the classical solution of $C([0,T_0],H^s)\cap C'([0,T_0],H^{s-2})$ with $s>d/2+2$.