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<p>We construct a local in time spatially real-analytic solution to the 2D and 3D stochastic Navier–Stokes equation driven by a spatially real-analytic multiplicative and transport noise but emanating from an initial condition that is only required to have bounded enstrophy. We also establish the exponential decay (in a weighted norm) of the finite-dimensional Galerkin approximation, with respect to its maximum wavenumber, to the strong pathwise solution of the stochastic Navier–Stokes equation. This decay is uniform in time, uniform with respect to the initial enstrophy, and uniform in the noise coefficients.</p>

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Spatial analyticity and exponential decay of Fourier modes for the stochastic Navier-Stokes equation

  • 期刊论文

  • 发表日期：

    2025年8月11日

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  • Dan Crisan,
  • Prince Romeo Mensah

摘要

We construct a local in time spatially real-analytic solution to the 2D and 3D stochastic Navier–Stokes equation driven by a spatially real-analytic multiplicative and transport noise but emanating from an initial condition that is only required to have bounded enstrophy. We also establish the exponential decay (in a weighted norm) of the finite-dimensional Galerkin approximation, with respect to its maximum wavenumber, to the strong pathwise solution of the stochastic Navier–Stokes equation. This decay is uniform in time, uniform with respect to the initial enstrophy, and uniform in the noise coefficients.