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.
Exact results on stationary turbulence in 2D: consequences of vorticity con- servation[J]
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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.