Profiles for bounded solutions of dispersive equations, with applications to energy-critical wave and Schr\"odinger equations
Profiles for bounded solutions of dispersive equations, with applications to energy-critical wave and Schr\"odinger equations
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色散方程有界解的轮廓，及其在能量临界波和薛定格方程中的应用
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
F. Merle
中科院分区：
文献类型：
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作者：
Thomas Duyckaerts;C. Kenig;F. Merle
考虑聚焦、能量临界波动方程的有界解，它不散射成线性解。我们证明了这个解在弱意义上收敛，沿着时间序列，直到缩放和空间平移，收敛到孤立波的和。这一结果是基于剖面分解的一种新的一般紧度/刚性论证的结果。并给出了该方法在能量临界Schr\ odinger方程中的一个应用。
Consider a bounded solution of the focusing, energy-critical wave equation that does not scatter to a linear solution. We prove that this solution converges in some weak sense, along a sequence of times and up to scaling and space translation, to a sum of solitary waves. This result is a consequence of a new general compactness/rigidity argument based on profile decomposition. We also give an application of this method to the energy-critical Schr\"odinger equation.
将球外部的波图松弛为所有数据的谐波图
影响因子：
2.2
作者：
Kenig, Carlos E.;Lawrie, Andrew;Schlag, Wilhelm
通讯作者：
Schlag, Wilhelm