三维随机Navier-Stokes方程局部强解的时空逼近

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics Pub Date : 2022-11-30 DOI:10.48550/arXiv.2211.17011

D. Breit, Alan Dodgson

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引用次数: 0

摘要

摘要我们考虑环面上的三维随机Navier-Stokes方程。我们的主要结果涉及局部强路径解的时间和时空离散化。我们证明了能量误差相对于概率收敛的最优收敛速度，即在空间上（高达）1阶的收敛和在时间上（高至）1/2阶的收敛。这一结果证明了（时间离散的）解可能会爆炸。我们的方法基于（时间离散的）解的离散停止时间。

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Space-Time Approximation of Local Strong Solutions to the 3D Stochastic Navier–Stokes Equations

Abstract We consider the 3D stochastic Navier–Stokes equation on the torus. Our main result concerns the temporal and spatio-temporal discretisation of a local strong pathwise solution. We prove optimal convergence rates for the energy error with respect to convergence in probability, that is convergence of order (up to) 1 in space and of order (up to) 1/2 in time. The result holds up to the possible blow-up of the (time-discrete) solution. Our approach is based on discrete stopping times for the (time-discrete) solution.

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来源期刊

Computational Methods in Applied Mathematics MATHEMATICS, APPLIED-

CiteScore

2.40

自引率

7.70%

发文量

期刊介绍： The highly selective international mathematical journal Computational Methods in Applied Mathematics　(CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics. The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.