Global existence of wave maps in 1+2 dimensions with finite energy data
The authors prove the existence of a global weak solution of the Cauchy problem with initial data of finite energy for the wave map from \(\mathbb R\times\mathbb R^2\) into a compact Riemannian manifold. To get such a weak solution, they use a unique global solution of a viscous approximation problem with a parameter \(\varepsilon\) for a regularized wave map. The solution of the Cauchy problem is obtained as a weak limit of the above approximate solutions as \(\varepsilon\rightarrow 0\).
scientific article; zbMATH DE number 1127672