= Yudovich characteristic flow
{c}
{title2=$\dot X(t)=u(t,X(t))$}
For a planar Euler velocity obtained from vorticity in $L^\infty_{\mathrm{loc}}(dt;L^1\cap L^\infty)$, the <planar vorticity velocity kernel> gives a locally integrable speed bound and <log-Lipschitz modulus>. Spatial mollification gives existence of global trajectories; the <Osgood uniqueness criterion> gives uniqueness and continuous dependence. Measurability in time and an initial trace are needed. This establishes the flow for a fixed Euler solution; nonlinear uniqueness of the Euler solution itself requires further comparison arguments.
Back to article page
