Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Lower bounds on the Lyapunov exponent of linear PDEs driven by random velocity
Lyapunov exponents have been extensively studied in the context of fluid mechanics, particularly for the Euler and Navier-Stokes equations. In this regard, the lower bounds of Lyapunov exponents are known to serve as a benchmark for chaos and turbulence. We introduce two primary models in fluid mechanics: passive scalar advection and linearized stochastic Navier-Stokes equations, and prove the lower bounds of their Lyapunov exponents, which are quantitative in the diffusion parameter. Our result provides a typical filamentation length scale, which partially answers the Bachelor conjecture. The proof relies on the high-frequency stochastic instability of the projective process via a detailed analysis of its spectral median. This is joint work with Martin Hairer, Sam Punshon-Smith, and Tommaso Rosati.
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