Global Well-Posedness and Regularity of Stochastic 3D Burgers Equation with Multiplicative Noise (Zhao Dong)

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09 20, 2023

  By utilizing 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.



  SIAM Journal on Mathematical Analysis, Volume 55, Issue 3 (2023)



  Zhao Dong

  RCSDS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.



  Boling Guo

  Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China.


  Jiang-Lun Wu

  Department of Mathematics, Computational Foundry, Swansea University, Swansea SA1 8EN, UK.


  Guoli Zhou

  School of Statistics and Mathematics, Chongqing University, Chongqing 400044, China.



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