Peer-reviewedCC BYCommunications in Mathematical Physics
A Universal Total Anomalous Dissipator
- 1Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, USA
- 2Courant Institute of Mathematical Sciences, New York University, New York City, USA
Abstract
For all α ∈ (0,1) α ∈ ( 0 , 1 ) , we construct an explicit divergence-free vector field V∈ L∞ tCα x ∩ C(α )/(1−α )t L∞ x V ∈ L t ∞ C x α ∩ C t α 1 - α L x ∞ so that the solutions to the drift–diffusion equations ∂ tθ κ −κ Δ θ κ +V· ∇ θ κ =0 ∂ t θ κ - κ Δ θ κ + V · ∇ θ κ = 0 exhibit asymptotic total dissipation for all mean-zero initial data: lim κ → 0‖ θ κ (1,· )‖ L2=0 lim κ → 0 ‖ θ κ ( 1 , · ) ‖ L 2 = 0 . Additionally, we give explicit rates in κ κ and uniform dependence on initial data.
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BibTeX
@article{hesschilds2026universal,
title = {{A Universal Total Anomalous Dissipator}},
author = {Elias Hess-Childs and Keefer Rowan},
journal = {Communications in Mathematical Physics},
year = {2026},
month = oct,
doi = {10.1007/s00220-026-05771-6},
url = {https://doi.org/10.1007/s00220-026-05771-6},
note = {CC BY},
}
RIS
TY - JOUR
TI - A Universal Total Anomalous Dissipator
AU - Elias Hess-Childs
AU - Keefer Rowan
PY - 2026
DA - 2026/10/28
JO - Communications in Mathematical Physics
DO - 10.1007/s00220-026-05771-6
UR - https://doi.org/10.1007/s00220-026-05771-6
AB - For all α ∈ (0,1) α ∈ ( 0 , 1 ) , we construct an explicit divergence-free vector field V∈ L^∞ _tC^α _x ∩ C^(α )/(1−α )_t L^∞ _x V ∈ L t ∞ C x α ∩ C t α 1 - α L x ∞ so that the solutions to the drift–diffusion equations ∂ _tθ ^κ −κ Δ θ ^κ +V· ∇ θ ^κ =0 ∂ t θ κ - κ Δ θ κ + V · ∇ θ κ = 0 exhibit asymptotic total dissipation for all mean-zero initial data: lim _κ → 0‖ θ ^κ (1,· )‖ _L^2=0 lim κ → 0 ‖ θ κ ( 1 , · ) ‖ L 2 = 0 . Additionally, we give explicit rates in κ κ and uniform dependence on initial data.
SN - 0010-3616
SN - 1432-0916
ER -