Uniqueness of weak solution for Chern-Simons-Dirac equations in R1Â +Â 1

We study the uniqueness of weak solution in Lloc∞([0,+∞);L2(R1)) for initial value problem of Chern-Simons-Dirac equations. We first derive the equations for the difference between two weak solutions and establish the existence of the solution to initial value problem to its adjoint system. Then we apply Holmgren's method to prove that the weak solution in Lloc∞([0,+∞);L2(R1)) to initial value problem of Chern-Simons-Dirac equations is unique.