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Global Well-Posedness and Regularity of Stochastic 3D Burgers Equation with Multiplicative Noise
SIAM Journal on Mathematical Analysis, Volume: 55, Issue: 3, Pages: 1847 - 1882
Swansea University Author: Jiang-lun Wu
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© The Author(s) 2023. Released under the terms of a CC BY 4.0 license.
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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...
Published in: | SIAM Journal on Mathematical Analysis |
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ISSN: | 0036-1410 1095-7154 |
Published: |
Society for Industrial & Applied Mathematics (SIAM)
2023
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Online Access: |
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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. |
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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 |