Uniform-in-diffusivity mixing by shear flows: stochastic and dynamical perspectives
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914380935856128 |
|---|---|
| author | Liss, Kyle L. Luan, Kunhui |
| author_facet | Liss, Kyle L. Luan, Kunhui |
| contents | We study passive scalar mixing by parallel shear flows in the presence of weak molecular diffusion. We recover the sharp uniform-in-diffusivity mixing rate for shear flows with finitely many critical points, recently proven in [1]. Our approach is based on the stochastic representation formula of the associated advection-diffusion equation and yields two short proofs. The first uses a stochastic integration-by-parts argument and gives optimal mixing under the weakest regularity assumption required in the zero-diffusion case, answering Question II in [1, Section 4]. The second adopts a dynamical systems perspective and provides a proof of shear-induced mixing that, to our knowledge, is new even in the zero-diffusivity setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09238 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uniform-in-diffusivity mixing by shear flows: stochastic and dynamical perspectives Liss, Kyle L. Luan, Kunhui Analysis of PDEs Dynamical Systems Probability 35Q35, 60J60, 37A25 We study passive scalar mixing by parallel shear flows in the presence of weak molecular diffusion. We recover the sharp uniform-in-diffusivity mixing rate for shear flows with finitely many critical points, recently proven in [1]. Our approach is based on the stochastic representation formula of the associated advection-diffusion equation and yields two short proofs. The first uses a stochastic integration-by-parts argument and gives optimal mixing under the weakest regularity assumption required in the zero-diffusion case, answering Question II in [1, Section 4]. The second adopts a dynamical systems perspective and provides a proof of shear-induced mixing that, to our knowledge, is new even in the zero-diffusivity setting. |
| title | Uniform-in-diffusivity mixing by shear flows: stochastic and dynamical perspectives |
| topic | Analysis of PDEs Dynamical Systems Probability 35Q35, 60J60, 37A25 |
| url | https://arxiv.org/abs/2603.09238 |