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The Eulerian limit for 2D statistical hydrodynamics. (English) Zbl 1157.76319
Summary: We consider the 2D Navier-Stokes system, perturbed by a white in time random force, proportional to the square root of the viscosity. We prove that under the limit “time to infinity, viscosity to zero” each of its (random) solution converges in distribution to a non-trivial stationary process, formed by solutions of the (free) Euler equation, while the Reynolds number grows to infinity. We study the convergence and the limiting solutions.

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations
35R60 PDEs with randomness, stochastic partial differential equations
60H40 White noise theory
76M35 Stochastic analysis applied to problems in fluid mechanics
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