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On the optimal decay rate of global solutions to the convection-diffusion equation with zero-mass initial data
Abstract
We consider the optimal decay rate of global solutions to the convection-diffusion equation with zero-mass initial data. We establish an improved decay estimate of the global solutions under the zero-mass condition. Moreover, we derive a self-similar asymptotic profile of the global solutions. This result shows that the improved decay rate is optimal and provides a necessary and sufficient condition for attaining this decay rate.
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BibTeX
@misc{huang2026optimal,
title = {{On the optimal decay rate of global solutions to the convection-diffusion equation with zero-mass initial data}},
author = {Yi C. Huang and Ryunosuke Kusaba},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.05158},
eprint = {2607.05158},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.05158},
}
RIS
TY - UNPB
TI - On the optimal decay rate of global solutions to the convection-diffusion equation with zero-mass initial data
AU - Yi C. Huang
AU - Ryunosuke Kusaba
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2607.05158
UR - https://arxiv.org/abs/2607.05158
AB - We consider the optimal decay rate of global solutions to the convection-diffusion equation with zero-mass initial data. We establish an improved decay estimate of the global solutions under the zero-mass condition. Moreover, we derive a self-similar asymptotic profile of the global solutions. This result shows that the improved decay rate is optimal and provides a necessary and sufficient condition for attaining this decay rate.
ER -