受随机噪声强迫的三维磁流体力学系统定律中的非唯一性

IF 1 3区数学 Q1 MATHEMATICS

Potential Analysis Pub Date : 2024-04-13 DOI:10.1007/s11118-024-10128-6

Kazuo Yamazaki

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引用次数: 0

摘要

我们证明了三维磁流体力学系统的非唯一性规律，该系统受加法和线性乘法随机噪声的影响，具有粘性扩散和磁性扩散，两者都比完全拉普拉斯弱。我们对速度方程和磁场方程进行凸积分，以获得概率强解类中的非唯一性规律。

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Non-uniqueness in law of three-dimensional magnetohydrodynamics system forced by random noise

We prove non-uniqueness in law of the three-dimensional magnetohydrodynamics system that is forced by random noise of an additive and a linear multiplicative type and has viscous and magnetic diffusion, both of which are weaker than a full Laplacian. We apply convex integration to both equations of velocity and magnetic fields in order to obtain the non-uniqueness in law in the class of probabilistically strong solutions.

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来源期刊

Potential Analysis 数学-数学

CiteScore

2.20

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original papers dealing with potential theory and its applications, probability theory, geometry and functional analysis and in particular estimations of the solutions of elliptic and parabolic equations; analysis of semi-groups, resolvent kernels, harmonic spaces and Dirichlet forms; Markov processes, Markov kernels, stochastic differential equations, diffusion processes and Levy processes; analysis of diffusions, heat kernels and resolvent kernels on fractals; infinite dimensional analysis, Gaussian analysis, analysis of infinite particle systems, of interacting particle systems, of Gibbs measures, of path and loop spaces; connections with global geometry, linear and non-linear analysis on Riemannian manifolds, Lie groups, graphs, and other geometric structures; non-linear or semilinear generalizations of elliptic or parabolic equations and operators; harmonic analysis, ergodic theory, dynamical systems; boundary value problems, Martin boundaries, Poisson boundaries, etc.