On the blowup of solutions for a nonlocal multi-dimensional transport equation
Analysis of PDEs
2026-03-03 v2
Abstract
In this paper, we revisit the problem of finite-time blowup for a multi-dimensional nonlocal transport equation studied in [Dong, Adv. Math. 264 (2014) 747-761]. Inspired by a one-dimensional analogous model considered in [Li-Rodrigo, Adv. Math. 374 (2020) 1-26], we establish a new weighted nonlinear inequality implying the blow-up by a completely real variable based technique. In particular, an inequality for the Riesz transform is obtained.
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@article{arxiv.2403.06449,
title = {On the blowup of solutions for a nonlocal multi-dimensional transport equation},
author = {Wanwan Zhang},
journal= {arXiv preprint arXiv:2403.06449},
year = {2026}
}
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