In pde, it seems to me all kinds of equations about nature phenomena have the property that time and space derivatives are separate. For example, u_t = u_xx, heat equation. So I wonder, is that always the case in nature? I mean, do you guys ever see equation describing real nature mechanism but has mixed derivatives involved, ie, has a term like u_tx? If not, is there a reason for that? This might be a silly question, but thanks in advance.