2022
DOI: 10.3934/dcdsb.2021154
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Abstract: We introduce a Gaussian measure formally preserved by the 2dimensional Primitive Equations driven by additive Gaussian noise. Under such measure the stochastic equations under consideration are singular: we propose a solution theory based on the techniques developed by Gubinelli and Jara in [15] for a hyperviscous version of the equations.

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“…It is worth to mention that, for dissipative dynamics as the Navier-Stokes equations, it may be necessary to perturb the system with an additive noise in order to produce statistically relevant stationary solutions (see for instance [1,8] on the Navier-Stokes system and [13] on Primitive equations). Also, at the moment we are not able to produce out-of-equilibrium solutions (not even at the discrete level).…”
Section: Introductionmentioning
confidence: 99%
“…It is worth to mention that, for dissipative dynamics as the Navier-Stokes equations, it may be necessary to perturb the system with an additive noise in order to produce statistically relevant stationary solutions (see for instance [1,8] on the Navier-Stokes system and [13] on Primitive equations). Also, at the moment we are not able to produce out-of-equilibrium solutions (not even at the discrete level).…”
Section: Introductionmentioning
confidence: 99%