The top Lyapunov exponent of the Lagrangian flow for 2D incompressible Navier-Stokes equations driven by mildly degenerate noise on low modes is strictly positive.
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General quantitative conditions are established for the existence of a unique invariant probability measure and exponential ergodicity of Markov semigroups for stochastic evolution equations with locally monotone drift and degenerate additive Wiener noise, together with moment estimates and Wasserst
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Lagrangian chaos for the 2D Navier-Stokes equations driven by mildly degenerate noise
The top Lyapunov exponent of the Lagrangian flow for 2D incompressible Navier-Stokes equations driven by mildly degenerate noise on low modes is strictly positive.
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Ergodicity and mixing for locally monotone stochastic evolution equations
General quantitative conditions are established for the existence of a unique invariant probability measure and exponential ergodicity of Markov semigroups for stochastic evolution equations with locally monotone drift and degenerate additive Wiener noise, together with moment estimates and Wasserst