受随机噪声影响的输运-扩散方程规律的非唯一性

IF 2.4 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2024-10-01 DOI:10.1016/j.jde.2024.09.046

Ujjwal Koley , Kazuo Yamazaki

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引用次数: 0

摘要

我们考虑了由三种随机噪声强迫的输运-扩散方程：加法噪声、伊藤解释的线性乘法噪声和斯特拉顿诺维奇解释的输运噪声。通过修改为概率设置的凸积分，我们证明了在 Sobolev 空间中具有空间正则性的无发散向量场的存在性，以及在 Lebesgue 空间中具有空间正则性的输运扩散方程的相应解，并因此证明了在时间上全局概率强解的非唯一性。

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Non-uniqueness in law of transport-diffusion equation forced by random noise

We consider a transport-diffusion equation forced by random noise of three types: additive, linear multiplicative in Itô's interpretation, and transport in Stratonovich's interpretation. Via convex integration modified to probabilistic setting, we prove existence of a divergence-free vector field with spatial regularity in Sobolev space and corresponding solution to a transport-diffusion equation with spatial regularity in Lebesgue space, and consequently non-uniqueness in law at the level of probabilistically strong solutions globally in time.

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来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics