径向情况下能量临界非线性波动方程的孤立子解

IF 2.4 1区数学 Q1 MATHEMATICS

Annals of Pde Pub Date : 2023-10-06 DOI:10.1007/s40818-023-00159-4

Jacek Jendrej, Andrew Lawrie

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引用次数: 5

摘要

我们考虑了空间维（D\ge4\）中径向对称初始数据的聚焦能量临界非线性波动方程。这个方程有一个独特的（直到符号和尺度）非平凡的有限能量平稳解W，称为基态。我们证明了每个具有有界能量范数的有限能量解在时间上连续地分解为基态和自由辐射的渐近解耦副本的有限叠加。

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Soliton Resolution for the Energy-Critical Nonlinear Wave Equation in the Radial Case

We consider the focusing energy-critical nonlinear wave equation for radially symmetric initial data in space dimensions \(D \ge 4\). This equation has a unique (up to sign and scale) nontrivial, finite energy stationary solution W, called the ground state. We prove that every finite energy solution with bounded energy norm resolves, continuously in time, into a finite superposition of asymptotically decoupled copies of the ground state and free radiation.

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来源期刊

Annals of Pde Mathematics-Geometry and Topology

CiteScore

3.70

自引率

3.60%

发文量