On the optimal decay rate of global solutions to the convection-diffusion equation with zero-mass initial data

Yi C. Huang; Ryunosuke Kusaba

On the optimal decay rate of global solutions to the convection-diffusion equation with zero-mass initial data

Analysis of PDEs 2026-07-06 v1

Authors: Yi C. Huang , Ryunosuke Kusaba

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 provides necessary and sufficient conditions for attaining the improved decay rate and shows that the decay rate is optimal.

Keywords

convection-diffusion equation zero-mass initial data optimal decay rate global solutions self-similar asymptotic profile

Cite

@article{arxiv.2607.05158,
  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},
  journal= {arXiv preprint arXiv:2607.05158},
  year   = {2026}
}

Comments

21 pages