标题： Skyrme波映射的衰减 显示英文标题

标题： Decay for Skyrme wave maps

摘要： 我们考虑Skyrme和Adkins-Nappi方程的整体解的衰减问题。 我们证明，任何有界能量解的Skyrme（或Adkins-Nappi）方程的相关能量在光锥外（在径向坐标中）趋于零。 此外，我们证明了任何小解的适当多项式加权能量，当这些能量被限制时，会趋于零。 证明包括找到三个新的类似virial的估计，其中一个用于光锥外部，基于解的能量，另一个更微妙的virial恒等式用于加权能量，基于动量型量的修改。 显示英文摘要

摘要： We consider the decay problem for global solutions of the Skyrme and Adkins-Nappi equations. We prove that the energy associated to any bounded energy solution of the Skyrme (or Adkins-Nappi) equation decays to zero outside the light cone (in the radial coordinate). Furthermore, we prove that suitable polynomial weighted energies of any small solution decays to zero when these energies are bounded. The proof consists of finding three new virial type estimates, one for the exterior of the light cone, based on the energy of the solution, and a more subtle virial identity for the weighted energies, based on a modification of momentum type quantities.