Globally stable blowup profile for supercritical wave maps in all dimensions.

IF 2.1 2区数学 Q1 MATHEMATICS Calculus of Variations and Partial Differential Equations Pub Date : 2025-01-01 Epub Date: 2025-01-06 DOI:10.1007/s00526-024-02901-7

Irfan Glogić

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引用次数: 0

Abstract

We consider wave maps from the $(1 + d)$ -dimensional Minkowski space into the d-sphere. It is known from the work of Bizoń and Biernat (Commun Math Phys 338(3): 1443-1450, 2015) that in the energy-supercritical case, i.e., for $d \geq 3$ , this model admits a closed-form corotational self-similar blowup solution. We show that this blowup profile is globally nonlinearly stable for all $d \geq 3$ , thereby verifying a perturbative version of the conjecture posed in Bizoń and Biernat (Commun Math Phys 338(3): 1443-1450, 2015) about the generic large data blowup behavior for this model. To accomplish this, we develop a novel stability analysis approach based on similarity variables posed on the whole space $R^{d}$ . As a result, we draw a general road map for studying spatially global stability of self-similar blowup profiles for nonlinear wave equations in the radial case for arbitrary dimension $d \geq 3$ .

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全维超临界波图的全局稳定爆破剖面。

我们考虑从（1 + d）维闵可夫斯基空间到d球的波映射。从bizoze和Biernat的工作可知（commath Phys 338(3): 1443- 1450,2015），在能量超临界情况下，即当d≥3时，该模型承认一个封闭形式的同向自相似爆破解。我们证明，对于所有d≥3，该爆炸轮廓是全局非线性稳定的，从而验证了bizoze和Biernat （common Math Phys 338(3): 1443- 1450,2015）提出的关于该模型的一般大数据爆炸行为的猜想的摄动版本。为了实现这一目标，我们提出了一种基于整个空间R d上的相似性变量的稳定性分析方法。本文为研究任意维数d≥3的径向情况下非线性波动方程的自相似爆破剖面的空间全局稳定性提供了一个总体思路。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Calculus of Variations and Partial Differential Equations 数学-数学

CiteScore

3.30

自引率

4.80%

发文量

224

审稿时长

6 months

期刊介绍： Calculus of variations and partial differential equations are classical, very active, closely related areas of mathematics, with important ramifications in differential geometry and mathematical physics. In the last four decades this subject has enjoyed a flourishing development worldwide, which is still continuing and extending to broader perspectives. This journal will attract and collect many of the important top-quality contributions to this field of research, and stress the interactions between analysts, geometers, and physicists. The field of Calculus of Variations and Partial Differential Equations is extensive; nonetheless, the journal will be open to all interesting new developments. Topics to be covered include: - Minimization problems for variational integrals, existence and regularity theory for minimizers and critical points, geometric measure theory - Variational methods for partial differential equations, optimal mass transportation, linear and nonlinear eigenvalue problems - Variational problems in differential and complex geometry - Variational methods in global analysis and topology - Dynamical systems, symplectic geometry, periodic solutions of Hamiltonian systems - Variational methods in mathematical physics, nonlinear elasticity, asymptotic variational problems, homogenization, capillarity phenomena, free boundary problems and phase transitions - Monge-Ampère equations and other fully nonlinear partial differential equations related to problems in differential geometry, complex geometry, and physics.