Wednesday, June 16, 2021 - 14:00 in ZOOM - Video Conference
Stabilization by transport noise and enhanced dissipation in the Kraichnan model
A talk in the Bielefeld Stochastic Afternoon series by
Ivan Yaroslavtsev from MPI Leipzig
| Abstract: |
Please contact stochana@math.uni-bielefeld.de for Meeting-ID and Password.
Thanks to the work of Arnold, Crauel, and Wihstutz it is known that for any self-adjoint operator $T$ acting on a finite dimensional space with the negative trace the corresponding linear equation $dx_t=Tx_tdt$ can be stabilized by a noise, i.e. there exists operator-valued Brownian motion $W$ such that the solution of $dx_t + d Wx_t=Tx_tdt$ vanishes a.s. for any initial value $x_0=x$. The goal of the talk is to extend this theorem to infinite dimensions. Namely, it is proven that the equation $du_t=(\Delta + C)u_tdt$ can be noise stabilized and that an arbitrary large exponential rate of decay can be reached. The sufficient conditions on the noise are shown to be satisfied by the so-called Kraichnan model for stochastic transport of passive scalars in turbulent fluids. This talk is based on joint work with Prof. Benjamin Gess (MPI MiS and Bielefeld University).
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