Work

Stabilization by transport noise and enhanced dissipation in the Kraichnan model

Year: 2025

Type: article

Abstract: Stabilization and sufficient conditions for mixing by stochastic transport are shown. More precisely, given a second-order linear operator with possibly unstable eigenvalues on a smooth compact Riemannian manifold, it is shown that the inclusion of transport noise can imply global asymptotic stability. Moreover, it is shown that an arbitrary large exponential rate of convergence can be reached, implying enhanced dissipation. The sufficient conditions are shown to be satisfied by the so-called Kraichnan model for stochastic transport of passive scalars in turbulent fluids. In addition, an example is given showing that it can be sufficient to force four modes in order to induce stabilization.

Source: Journal of Evolution Equations

DOI: 10.1007/s00028-025-01066-w

Authors: Benjamin Gess, Ivan Yaroslavtsev

Institutions: Bielefeld University, Max Planck Institute for Mathematics in the Sciences

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: Deutsche Forschungsgemeinschaft, Max-Planck-Gesellschaft