论文标题
关于各种临界波方程的非辐射溶液的分类
On classification of non-radiative solutions for various energy-critical wave equations
论文作者
论文摘要
能量关键波方程的非辐射溶液使得它们在外部区域中的能量$ | x |> r+| t | $在两个时间方向上渐近地消失。这一概念是由Duyckaerts，Kenig和Merle（J。Eur。Math。Soc。，2011年）提出的，在径向案例中为这些方程式解决了这些方程的孤儿解决方案一直是关键。在本文中，我们首先将其在Infinity的渐近行为进行分类，这表明它们对应于$ k $ - 参数的解决方案家族，其中$ k $取决于维度。这概括了先前的结果（Duyckaerts，Kenig和Merle，Camb。J.Math。，2013年，以及杜伊卡特，Kenig，Martel和Merle，Comm。Math。Phys。，2022年），分别为三个和四个维度）。然后，我们建立了这些解决方案的独特最大扩展。
Non-radiative solutions of energy critical wave equations are such that their energy in an exterior region $|x|>R+|t|$ vanishes asymptotically in both time directions. This notion, introduced by Duyckaerts, Kenig and Merle (J. Eur. Math. Soc., 2011), has been key in solving the soliton resolution conjecture for these equations in the radial case. In the present paper, we first classify their asymptotic behaviour at infinity, showing that they correspond to a $k$-parameters family of solutions where $k$ depends on the dimension. This generalises the previous results (Duyckaerts, Kenig and Merle, Camb. J. Math., 2013 and Duyckaerts, Kenig, Martel and Merle, Comm. Math. Phys., 2022) in three and four dimensions. We then establish a unique maximal extension of these solutions.
