Free transport equation
= Free transport equation
{title2=$\partial_tf+v\cdot\nabla_xf=0$}
Particles keep their velocity and move along straight trajectories. The <method of characteristics> gives $f(t,x,v)=f_0(x-tv,v)$. The shear preserves <Lebesgue measure> and every <Lp norm>. Compact initial <support> remains compact at each finite time, but need not remain in one compact set for all times.