 Yudovich characteristic flow

For a planar Euler velocity obtained from vorticity in $L_{\mathrm{loc}}^{\infty }(dt;L^1\cap L^{\infty })$, 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.