Ill-posedness issue on a multidimensional chemotaxis equations in the critical Besov spaces

Jinlu Li; Yanghai Yu; Weipeng Zhu

Ill-posedness issue on a multidimensional chemotaxis equations in the critical Besov spaces

Analysis of PDEs 2022-11-22 v3

Authors: Jinlu Li , Yanghai Yu , Weipeng Zhu

Abstract

In this paper, we aim to solving the open question left in [Nie, Yuan: Nonlinear Anal 196 (2020); J. Math. Anal. Appl 505 (2022)) and Xiao, Fei: J. Math. Anal. Appl 514 (2022)]. We prove that a multidimensional chemotaxis system is ill-posedness in $\dot{B}_{2d, r}^{-\frac{3}{2}} \times\big(\dot{B}_{2d, r}^{-\frac{1}{2}}\big)^{d}$ when $1\leq r<d$ due to the lack of continuity of the solution.

Keywords

chemotaxis system ill-posedness critical besov spaces multidimensional equations continuity of solution

Cite

@article{arxiv.2206.02668,
  title  = {Ill-posedness issue on a multidimensional chemotaxis equations in the critical Besov spaces},
  author = {Jinlu Li and Yanghai Yu and Weipeng Zhu},
  journal= {arXiv preprint arXiv:2206.02668},
  year   = {2022}
}

Comments

17 pages, to appear Journal of Geometric Analysis

Related papers

View all related →