On a multi-dimensional transport equation with nonlocal velocity and fractional dissipation

Wanwan Zhang

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arXiv · 2405.16364

On a multi-dimensional transport equation with nonlocal velocity and fractional dissipation

Wanwan Zhang

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Abstract

This paper aims to investigate a multi-dimensional transport equation with nonlocal velocity and fractional dissipation.The balance between the nonlinearity and dissipation gives rise to three different cases, namely the subcritical, critical and supercritical ranges. We study those three cases and obtain a set of results containing local well-posedness, global smoothness, eventual regularity and finite-time blowup of smooth solutions.

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Wanwan Zhang. 2024-05-25. On a multi-dimensional transport equation with nonlocal velocity and fractional dissipation. https://arxiv.org/abs/2405.16364

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