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<p>In this work, we study convection–diffusion equations in the cases of bounded drifts and drifts induced by the gradient of a potential. We define a new notion of solution and prove its existence and uniqueness. Furthermore, we show the conservation of mass, the convergence to the initial data, and the strong maximum principle.</p>

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Existence and uniqueness of the solutions to convection–diffusion equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月21日

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  • Alireza Ataei

摘要

In this work, we study convection–diffusion equations in the cases of bounded drifts and drifts induced by the gradient of a potential. We define a new notion of solution and prove its existence and uniqueness. Furthermore, we show the conservation of mass, the convergence to the initial data, and the strong maximum principle.