English

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.

Keywords

Cite

@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}
}

Comments

Revisions