Year: 2025
Type: preprint
Abstract: For all $α\in(0,1)$, we construct an explicit divergence-free vector field $V\in L^\infty_tC^α_x \cap C^{\fracα{1-α}}_t L^\infty_x$ so that the solutions to the drift-diffusion equations $$\partial_tθ^κ-κΔθ^κ+V\cdot\nablaθ^κ=0$$ exhibit asymptotic total dissipation for all mean-zero initial data: $\lim_{κ\rightarrow 0}\|θ^κ(1,\cdot)\|_{L^2}=0$. Additionally, we give explicit rates in $κ$ and uniform dependence on initial data.
Source: arXiv (Cornell University)
Authors: Hess-Childs, Elias, Rowan, Keefer
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4407012559