Unique Continuation Property for the Coupled Ostrovsky System

IF 1 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2026-06-05 Epub Date: 2026-05-05 DOI:10.1002/mana.70147

Ricardo Córdoba, Alex M. Montes

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引用次数: 0

Abstract

In this paper, we establish a result of unique continuation for the coupled Ostrovsky system that models the evolution of long water waves with small amplitude in the presence of surface tension. More precisely, we will show that if $(u, v) = (u (x, t), v (x, t))$ is a solution of the nonlinear system, in a suitable function space, and $(u, v)$ vanishes on an open subset $Ω$ of $R \times [- T, T]$ , then $(u, v) \equiv 0$ in the horizontal component of $Ω$ . To state such property, we use a Carleman-type estimate for a differential operator $L$ related to the system. We prove the Carleman estimate using a particular version of the well-known Treves' inequality.

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耦合Ostrovsky系统的唯一延拓性质

本文建立了耦合Ostrovsky系统的唯一延拓结果，该系统模拟了在表面张力存在下小振幅长水波的演化。更准确地说，我们会证明如果(u, v) = (u (x, t), v (x，T)) $(u,v) =(u(x, t), v(x, t))$是非线性系统在合适的函数空间中的解，(u，v) $(u,v)$在R ×[−T， T] $\mathbb {R}\times [-T, T]$的开放子集Ω $\Omega$上消失，则（u, v）在Ω $\Omega$的水平分量中≡0 $(u,v)\equiv 0$。为了说明这一性质，我们使用了与系统相关的微分算子L $\mathcal {L}$的carleman型估计。我们使用著名的特里夫斯不等式的一个特殊版本来证明Carleman估计。

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

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index