Relaxation Enhancement by Time-Periodic Flows

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dc.creatorKiselev, Alexander
dc.creatorShterenberg, Roman
dc.creatorZlatos, Andrej
dc.date2007-06-29
dc.date.accessioned2026-07-07T08:13:08Z
dc.date.available2026-07-07T08:13:08Z
dc.descriptionWe study enhancement of diffusive mixing by fast incompressible time-periodic flows. The class of relaxation-enhancing flows that are especially efficient in speeding up mixing has been introduced in [2]. The relaxation-enhancing property of a flow has been shown to be intimately related to the properties of the dynamical system it generates. In particular, time-independent flows $u$ such that the operator $u \cdot \nabla$ has sufficiently smooth eigenfunctions are not relaxation-enhancing. Here we extend results of [2] to time-periodic flows $u(x,t)$ and in particular show that there exist flows such that for each fixed time the flow is Hamiltonian, but the resulting time-dependent flow is relaxation-enhancing. Thus we confirm the physical intuition that time dependence of a flow may aid mixing. We also provide an extension of our results to the case of a nonlinear diffusion model. The proofs are based on a general criterion for the decay of a semigroup generated by an operator of the form $Γ+iAL(t)$ with a negative unbounded self-adjoint operator $Γ$, a time-periodic self-adjoint operator-valued function $L(t)$, and a parameter $A>>1$.
dc.description11 pp
dc.identifierhttps://arxiv.org/abs/0706.4411
dc.identifierhttp://arxiv.org/abs/0706.4411
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/132696
dc.subjectAnalysis of PDEs
dc.subjectFunctional Analysis
dc.subjectSpectral Theory
dc.subject35K15; 35K55; 35K90
dc.titleRelaxation Enhancement by Time-Periodic Flows
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