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Book Sections Year : 2023

Modeling Under Location Uncertainty: A Convergent Large-Scale Representation of the Navier-Stokes Equations

Abstract

Abstract We construct martingale solutions for the stochastic Navier-Stokes equations in the framework of the modelling under location uncertainty (LU). These solutions are pathwise and unique when the spatial dimension is 2D. We then prove that if the noise intensity goes to zero, these solutions converge, up to a subsequence in dimension 3, to a solution of the deterministic Navier-Stokes equation. This warrants that the LU Navier-Stokes equations can be interpreted as a large-scale model of the deterministic Navier-Stokes equation.
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Dates and versions

hal-03910767 , version 1 (23-01-2023)

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Arnaud Debussche, Berenger Hug, Etienne Mémin. Modeling Under Location Uncertainty: A Convergent Large-Scale Representation of the Navier-Stokes Equations. Stochastic Transport in Upper Ocean Dynamics, 10, Springer International Publishing, pp.15-26, 2023, Mathematics of Planet Earth, ⟨10.1007/978-3-031-18988-3_2⟩. ⟨hal-03910767⟩
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