This article proves the ill-posedness of the Cauchy problem for the two-dimensional Keller–Segel model in Triebel–Lizorkin spaces, for . In particular, it is shown that solutions can develop norm inflation under certain settings in that the solution can become arbitrarily large after an arbitrarily short time even for small initial data.
Deng, Chao, and John Villavert. 2014. “Ill-Posedness of the Two-Dimensional Keller–Segel Model in Triebel–Lizorkin Spaces.” Nonlinear Analysis: Theory, Methods & Applications 95 (January): 38–49. https://doi.org/10.1016/j.na.2013.08.023.
Nonlinear Analysis: Theory, Methods & Applications