Diffusion in Fluid Flow: Dissipation Enhancement by Flows in 2D
| dc.creator | Zlatos, Andrej | |
| dc.date | 2007-01-04 | |
| dc.date.accessioned | 2026-07-07T07:38:35Z | |
| dc.date.available | 2026-07-07T07:38:35Z | |
| dc.description | We consider the advection-diffusion equation \[ ϕ_t + Au \cdot \nabla ϕ= Δϕ, \qquad ϕ(0,x)=ϕ_0(x) \] on $\bbR^2$, with $u$ a periodic incompressible flow and $A\gg 1$ its amplitude. We provide a sharp characterization of all $u$ that optimally enhance dissipation in the sense that for any initial datum $ϕ_0\in L^p(\bbR^2)$, $p<\infty$, and any $τ>0$, \[ \|ϕ(\cdot,τ)\|_{L^\infty(\bbR^2)} \to 0 \qquad \text{as $A\to\infty$.} \] Our characterization is expressed in terms of simple geometric and spectral conditions on the flow. Moreover, if the above convergence holds, it is uniform for $ϕ_0$ in the unit ball of $L^p(\mathbb{R}^2)$, $p<\infty$, and $\|\cdot\|_\infty$ can be replaced by any $\|\cdot\|_q$, $q>p$. Extensions to higher dimensions and applications to reaction-advection-diffusion equations are also considered. | |
| dc.description | 35 pp | |
| dc.identifier | https://arxiv.org/abs/math/0701123 | |
| dc.identifier | http://arxiv.org/abs/math/0701123 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121141 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Spectral Theory | |
| dc.title | Diffusion in Fluid Flow: Dissipation Enhancement by Flows in 2D | |
| dc.type | text |