Global existence and non-uniqueness for the Cauchy problem associated to 3D Navier–Stokes equations perturbed by transport noise

IF 1.4 3区数学 Q2 MATHEMATICS, APPLIED

Stochastics and Partial Differential Equations-Analysis and Computations Pub Date : 2023-10-30 DOI:10.1007/s40072-023-00318-5

Umberto Pappalettera

引用次数: 6

Abstract

Abstract We show global existence and non-uniqueness of probabilistically strong, analytically weak solutions of the three-dimensional Navier–Stokes equations perturbed by Stratonovich transport noise. We can prescribe either: (i) any divergence-free, square integrable intial condition; or (ii) the kinetic energy of solutions up to a stopping time, which can be chosen arbitrarily large with high probability. Solutions enjoy some Sobolev regularity in space but are not Leray–Hopf.

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输运噪声扰动下三维Navier-Stokes方程Cauchy问题的全局存在性和非唯一性

摘要给出了受stronovich输运噪声扰动的三维Navier-Stokes方程的概率强、解析弱解的全局存在性和非唯一性。我们可以规定:(i)任何无散度，平方可积的初始条件;或(ii)解在停止时间前的动能，可以大概率任意选择。解在空间中具有索博列夫正则性，但不是勒雷-霍普夫正则性。

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

Stochastics and Partial Differential Equations-Analysis and Computations Mathematics-Modeling and Simulation

CiteScore

2.70

自引率

13.30%

发文量

期刊介绍： Stochastics and Partial Differential Equations: Analysis and Computations publishes the highest quality articles presenting significantly new and important developments in the SPDE theory and applications. SPDE is an active interdisciplinary area at the crossroads of stochastic anaylsis, partial differential equations and scientific computing. Statistical physics, fluid dynamics, financial modeling, nonlinear filtering, super-processes, continuum physics and, recently, uncertainty quantification are important contributors to and major users of the theory and practice of SPDEs. The journal is promoting synergetic activities between the SPDE theory, applications, and related large scale computations. The journal also welcomes high quality articles in fields strongly connected to SPDE such as stochastic differential equations in infinite-dimensional state spaces or probabilistic approaches to solving deterministic PDEs.