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I'm stuck because I am not an expert in the field and I don't know where to start with such estimates :( If you can suggest me where to study these things that would be great.
@ChristianRemling: I've added your condition in my question; assume now to work under this additional hypothesis: do you see any reasonable way for this to work now?
could you just please elaborate a little your example of a divergence-free vector field $X$, with flow $f^t$? I think I don't quite get it yet. Many thanks.
@DeaneYang And Btw I'm having indeed quite a hard time reading your paper, but it is really worth every single minute spent. Really cannot say how much I appreciate your patience. Regards
@DeaneYang as your addendum points at.. Let's say that it is sufficient to solve my system using $E_1$ and $E_2+E_3$, that is $p=0,\;q=1$ using your notations. If I do this I come up again with an overdetermined system, indeed $E_1$ and $E_2+E_3$ are linearly dependent. But then modulo compatibility relations it is sufficient to check hyperbolicity just by inspecting the first equation. Did I understood correctly?
@DeaneYang Could you please give the references you were hinting at about invariant ways to detect hyperbolic differential systems? Thank you very much in advance
