科研之友
微信
新浪微博
Facebook
分享链接
摘要
We prove a uniqueness theorem for solutions to the wave map equation in the natural class, namely (u, partial derivative(t)u) is an element of C([0, T); (H) over dot(d/2)) x C-1([0, T); (H) over dot(d/2-1)) in dimension d %26gt;= 4. This is achieved by estimating the difference of two solutions at a lower regularity level. In order to reduce to the Coulomb gauge, one has to localize the gauge change in suitable cones, as well as to estimate the difference between the frames and connections associated with each solution and to take advantage of the assumption that the target manifold has bounded curvature.
- 出版日期2012-6
