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<p>For a class of evolution equations that possibly have only local in time solutions, we introduce a stochastic component that ensures that the solutions of the corresponding stochasticallys perturbed equations are global in time. The class of partial differential equations amenable for this type of treatment includes the 3D Navier-Stokes equation, the rotating shallow water equation (viscous and inviscid), 3D Euler equation (in vorticity form), 2D Burgers’ equation and many other fluid dynamics models.</p>

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Global solutions for stochastically controlled fluid dynamics models

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年10月10日

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  • Oana Lang,
  • Dan Crisan

摘要

For a class of evolution equations that possibly have only local in time solutions, we introduce a stochastic component that ensures that the solutions of the corresponding stochasticallys perturbed equations are global in time. The class of partial differential equations amenable for this type of treatment includes the 3D Navier-Stokes equation, the rotating shallow water equation (viscous and inviscid), 3D Euler equation (in vorticity form), 2D Burgers’ equation and many other fluid dynamics models.