Uniqueness of weak solutions of \(1+1\) dimensional wave maps (Q1961439)

The author studies the equations of wave maps from \((1+1)\)-dimensional Minkowsky space to any complete Riemannian manifold. It is proved that a finite energy distributional solution to the Cauchy problem is unique. The technique is based on previous works on quasilinear hyperbolic systems. The result shows that the \((1+1)\)-dimensional case is in sharp contrast with the \((3+1)\)-dimensional one where the weak solutions are not unique.