Transition from ergodic to explosive behavior in a family of stochastic differential equations

Abstract

We study a family of quadratic stochastic differential equations in the plane, motivated by applications to turbulent transport of heavy particles. Using Lyapunov functions, we find a critical parameter value ${\alpha }_1={\alpha }_2$ such that when ${\alpha }_2>{\alpha }_1$ the system is ergodic and when ${\alpha }_2<{\alpha }_1$ solutions are not defined for all times. Hörmander's hypoellipticity theorem and geometric control theory are also utilized.

35 pages, 6 figures

References in corpus (1)

• Ergodic properties of a model for turbulent dispersion of inertial particles

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