Abstract:We consider a fluid governed by the randomly forced 2D Navier-Stokes system. The force is bounded and highly degenerate, acting directly only on a small number of Fourier modes, and satisfies natural decomposability and observability properties. We prove that the Lagrangian flow associated with this system exhibits chaotic behavior, characterized by the strict positivity of the top Lyapunov exponent. To achieve this, we develop a new abstract criterion for random dynamical systems that enables one to derive the positivity of the top Lyapunov exponent and exponential mixing from controllability properties of the associated nonlinear and linearized deterministic systems. In particular, our mixing criterion removes the analyticity assumption required in previous works and establishes an exponential rate of convergence in the case where the unperturbed dynamics does not admit a unique globally stable equilibrium.
From: Vahagn Nersesyan [view email]
[v1]
Tue, 25 Jun 2024 14:58:43 UTC (36 KB)
[v2]
Fri, 15 Nov 2024 13:31:31 UTC (40 KB)
[v3]
Thu, 17 Sep 2026 14:03:12 UTC (48 KB)
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