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<p>In this paper, we study the stochastic Navier-Stokes equations driven by multiplicative noise. We demonstrate that the introduction of noise regularizes the system, enabling global solutions for small initial data. By employing a stochastic transformation technique, we reduce the problem to a deterministic PDE and establish existence through energy estimates and fixed-point methods. Our work extends classical deterministic results while providing new insights into fluid dynamics under random perturbations.</p>

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Global solutions to the Navier-Stokes equations with random diffusion

  • 期刊论文

  • 发表日期：

    2025年11月18日

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  • Mohamed Toumlilin

摘要

In this paper, we study the stochastic Navier-Stokes equations driven by multiplicative noise. We demonstrate that the introduction of noise regularizes the system, enabling global solutions for small initial data. By employing a stochastic transformation technique, we reduce the problem to a deterministic PDE and establish existence through energy estimates and fixed-point methods. Our work extends classical deterministic results while providing new insights into fluid dynamics under random perturbations.