Characteristic vector field
= Characteristic vector field
{title2=$a\partial_x+b\partial_y$}
For $au_x+bu_y=c$, the projected <vector field> $(a,b)$ has the <characteristic projections> as its integral curves. The lifted <vector field> is $(a,b,c)$ in $(x,y,u)$ coordinates. A vanishing projected <vector field> can obstruct a <classical solution> even when the lifted <vector field> does not vanish.