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The zero viscosity limit of stochastic Navier–Stokes flows

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  • Goodair, Daniel
  • Crisan, Dan

Abstract

We introduce an analogue to Kato’s Criterion regarding the inviscid convergence of weak solutions of the stochastic Navier–Stokes equations to the strong solution of the deterministic Euler equation. Our assumptions cover additive, multiplicative and transport type noise models. This is achieved firstly for the typical noise scaling of ν12, before considering a new parameter which approaches zero with viscosity but at a potentially different rate. We determine the implications of this for our criterion and clarify a sense in which the scaling by ν12 is optimal. The criterion applies in both two and three dimensions, with some technical simplifications in the 2D case.

Suggested Citation

  • Goodair, Daniel & Crisan, Dan, 2025. "The zero viscosity limit of stochastic Navier–Stokes flows," Stochastic Processes and their Applications, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:spapps:v:189:y:2025:i:c:s0304414925001589
    DOI: 10.1016/j.spa.2025.104717
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    References listed on IDEAS

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    1. Yasunori Maekawa & Anna Mazzucato, 2018. "The Inviscid Limit and Boundary Layers for Navier-Stokes Flows," Springer Books, in: Yoshikazu Giga & Antonín Novotný (ed.), Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, chapter 15, pages 781-828, Springer.
    2. Cipriano, Fernanda & Torrecilla, Iván, 2015. "Inviscid limit for 2D stochastic Navier–Stokes equations," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2405-2426.
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