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Global Well-Posedness and Regularity of Stochastic 3D Burgers Equation with Multiplicative Noise

Zhao Dong, Boling Guo, Jiang-lun Wu, Guoli Zhou Orcid Logo

SIAM Journal on Mathematical Analysis, Volume: 55, Issue: 3, Pages: 1847 - 1882

Swansea University Author: Jiang-lun Wu

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DOI (Published version): 10.1137/21m1413377

Abstract

By utilising the so-called Doss-Sussman transformation, we link our stochastic 3D Burgers equation with linear multiplicative noise to a random 3D Burger equation. With the help of techniques from partial differential equations (PDEs) and probability, we establish the global well-posedness of stocha...

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Published in: SIAM Journal on Mathematical Analysis
ISSN: 0036-1410 1095-7154
Published: Society for Industrial & Applied Mathematics (SIAM) 2023
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URI: https://cronfa.swan.ac.uk/Record/cronfa62323
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spelling 2025-06-05T11:24:34.5695245 v2 62323 2023-01-13 Global Well-Posedness and Regularity of Stochastic 3D Burgers Equation with Multiplicative Noise dbd67e30d59b0f32592b15b5705af885 Jiang-lun Wu Jiang-lun Wu true false 2023-01-13 By utilising the so-called Doss-Sussman transformation, we link our stochastic 3D Burgers equation with linear multiplicative noise to a random 3D Burger equation. With the help of techniques from partial differential equations (PDEs) and probability, we establish the global well-posedness of stochastic 3D Burgers with the diffusion coefficient being constant. Next, by developing a solution which is orthogonal with the gradient of coefficient of the noise, we extend the global well-posedness to a more general case in which the diffusion coefficient is spatial dependent, i.e., it is a function of the spatial variable.Our results and methodology pave a way to extend some regularity results of stochastic 1D Burgers equation to stochastic 3D Burgers equations. Journal Article SIAM Journal on Mathematical Analysis 55 3 1847 1882 Society for Industrial & Applied Mathematics (SIAM) 0036-1410 1095-7154 Stochastic 3D Burgers equations; regularity; maximum principle. 30 6 2023 2023-06-30 10.1137/21m1413377 COLLEGE NANME COLLEGE CODE Swansea University Other National Key R & D Program of China, National Natural Science Foundation of China 2020YFA0712700, 12090014, 11931004, 11971077 2025-06-05T11:24:34.5695245 2023-01-13T14:05:05.2260742 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Zhao Dong 1 Boling Guo 2 Jiang-lun Wu 3 Guoli Zhou 0000-0002-6599-1859 4 62323__26289__c3e9aada7b9945b0bddc0a8df34bce2c.pdf DongGuoWuZhou.pdf 2023-01-13T17:49:20.1200650 Output 394100 application/pdf Accepted Manuscript true © The Author(s) 2023. Released under the terms of a CC BY 4.0 license. true eng https://creativecommons.org/licenses/by/4.0/
title Global Well-Posedness and Regularity of Stochastic 3D Burgers Equation with Multiplicative Noise
spellingShingle Global Well-Posedness and Regularity of Stochastic 3D Burgers Equation with Multiplicative Noise
Jiang-lun Wu
title_short Global Well-Posedness and Regularity of Stochastic 3D Burgers Equation with Multiplicative Noise
title_full Global Well-Posedness and Regularity of Stochastic 3D Burgers Equation with Multiplicative Noise
title_fullStr Global Well-Posedness and Regularity of Stochastic 3D Burgers Equation with Multiplicative Noise
title_full_unstemmed Global Well-Posedness and Regularity of Stochastic 3D Burgers Equation with Multiplicative Noise
title_sort Global Well-Posedness and Regularity of Stochastic 3D Burgers Equation with Multiplicative Noise
author_id_str_mv dbd67e30d59b0f32592b15b5705af885
author_id_fullname_str_mv dbd67e30d59b0f32592b15b5705af885_***_Jiang-lun Wu
author Jiang-lun Wu
author2 Zhao Dong
Boling Guo
Jiang-lun Wu
Guoli Zhou
format Journal article
container_title SIAM Journal on Mathematical Analysis
container_volume 55
container_issue 3
container_start_page 1847
publishDate 2023
institution Swansea University
issn 0036-1410
1095-7154
doi_str_mv 10.1137/21m1413377
publisher Society for Industrial & Applied Mathematics (SIAM)
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description By utilising the so-called Doss-Sussman transformation, we link our stochastic 3D Burgers equation with linear multiplicative noise to a random 3D Burger equation. With the help of techniques from partial differential equations (PDEs) and probability, we establish the global well-posedness of stochastic 3D Burgers with the diffusion coefficient being constant. Next, by developing a solution which is orthogonal with the gradient of coefficient of the noise, we extend the global well-posedness to a more general case in which the diffusion coefficient is spatial dependent, i.e., it is a function of the spatial variable.Our results and methodology pave a way to extend some regularity results of stochastic 1D Burgers equation to stochastic 3D Burgers equations.
published_date 2023-06-30T05:09:47Z
_version_ 1851096707521052672
score 11.089386

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