随机旋转浅水模型的适定性

IF 1.4 4区数学 Q1 MATHEMATICS

Journal of Dynamics and Differential Equations Pub Date : 2024-01-01 Epub Date: 2023-01-20 DOI:10.1007/s10884-022-10243-1

Dan Crisan, Oana Lang

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引用次数: 0

摘要

本文研究了随机旋转浅水系统的拟合性质。霍尔姆（Proc R Soc A 471:20140963，2015）首次推导了该模型的无粘性版本，并根据霍尔姆（Proc R Soc A 471:20140963，2015）提出的列传输随机平流理论选择了噪声。该系统受到噪声的扰动，噪声由一个函数调制，该函数在寻求问题解决的规范中不是 Lipschitz 函数。我们证明，该系统有一个唯一的最大解，它连续地依赖于初始条件。我们还证明存在区间为严格正值，且解以正概率为全局。

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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Well-Posedness Properties for a Stochastic Rotating Shallow Water Model.

In this paper, we study the well-posedness properties of a stochastic rotating shallow water system. An inviscid version of this model has first been derived in Holm (Proc R Soc A 471:20140963, 2015) and the noise is chosen according to the Stochastic Advection by Lie Transport theory presented in Holm (Proc R Soc A 471:20140963, 2015). The system is perturbed by noise modulated by a function that is not Lipschitz in the norm where the well-posedness is sought. We show that the system admits a unique maximal solution which depends continuously on the initial condition. We also show that the interval of existence is strictly positive and the solution is global with positive probability.

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来源期刊

Journal of Dynamics and Differential Equations 数学-数学

CiteScore

3.30

自引率

7.70%

发文量

116

审稿时长

>12 weeks

期刊介绍： Journal of Dynamics and Differential Equations serves as an international forum for the publication of high-quality, peer-reviewed original papers in the field of mathematics, biology, engineering, physics, and other areas of science. The dynamical issues treated in the journal cover all the classical topics, including attractors, bifurcation theory, connection theory, dichotomies, stability theory and transversality, as well as topics in new and emerging areas of the field.