论文标题
为5D能量波动方程式构建激发的多solitons
Construction of excited multi-solitons for the 5D energy-critical wave equation
论文作者
论文摘要
对于5D关键性波方程，我们构建了具有共线速度的激动$ n $ - solitons，即方程式的解决方案$ u $ \ begin {equation*} \ lim_ {t \ to+\ infty} \ big | \ nabla_ { \ end {equation*}其中，对于$ n = 1，\ ldots，n $，$ q_n（t，x）$是lorentz的lorentz变换，是非脱位和充分衰减的兴奋状态的转换，每个状态具有不同但共线的速度。存在证明是遵循Martel-Merle和Côte-Martel为关键浪潮和非线性Klein-Gordon方程而开发的。特别是，我们依靠一种能量方法和线性化操作员的一般胁迫性能。
For the 5D energy-critical wave equation, we construct excited $N$-solitons with collinear speeds, i.e. solutions $u$ of the equation such that \begin{equation*} \lim_{t\to+\infty}\bigg\|\nabla_{t,x}u(t)-\nabla_{t,x}\bigg(\sum_{n=1}^{N}Q_{n}(t)\bigg)\bigg\|_{L^{2}}=0, \end{equation*} where for $n=1,\ldots,N$, $Q_n(t,x)$ is the Lorentz transform of a non-degenerate and sufficiently decaying excited state, each with different but collinear speeds. The existence proof follows the ideas of Martel-Merle and Côte-Martel developed for the energy-critical wave and nonlinear Klein-Gordon equations. In particular, we rely on an energy method and on a general coercivity property for the linearized operator.
