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

被引：7

作者：

Jendrej, Jacek ^{[1
,2
]}

Lawrie, Andrew ^{[3
]}

机构：

[1] Univ Sorbonne Paris Nord, CNRS, 99 Jean Baptiste Clement, F-93430 Villetaneuse, France

[2] Univ Sorbonne Paris Nord, LAGA, 99 Jean Baptiste Clement, F-93430 Villetaneuse, France

[3] MIT, Dept Math, 77 Massachusetts Ave 2-267, Cambridge, MA 02139 USA

来源：

ANNALS OF PDE | 2023年 / 9卷 / 02期

关键词：

Soliton resolution; Multi-soliton; Wave maps; Energy-critical; BLOW-UP SOLUTIONS; SEMILINEAR WAVE; HARMONIC MAPS; THRESHOLD SOLUTIONS; 2-BUBBLE SOLUTIONS; GLOBAL-SOLUTIONS; GROUND-STATE; SCATTERING; REGULARITY; PROFILES;

D O I：

10.1007/s40818-023-00159-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the focusing energy-critical nonlinear wave equation for radially symmetric initial data in space dimensions D >= 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.

引用

页数：117

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