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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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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 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.
Keywords: Stochastic 3D Burgers equations; regularity; maximum principle.
College: Faculty of Science and Engineering
Funders: National Key R & D Program of China, National Natural Science Foundation of China
Issue: 3
Start Page: 1847
End Page: 1882

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