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

Yi C. Huang; Ryunosuke Kusaba

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arXiv · 2607.05158

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

Yi C. Huang·Ryunosuke Kusaba

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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.

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Yi C. Huang, Ryunosuke Kusaba. 2026-07-06. On the optimal decay rate of global solutions to the convection-diffusion equation with zero-mass initial data. https://arxiv.org/abs/2607.05158

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