For a class of drift-diffusion systems Kurokiba et al. [M. Kurokiba, T. Nagai, T. Ogawa, The uniform boundedness and threshold for the global existence of the radial solution to a drift-diffusion system, Commun. Pure Appl. Anal. 5 (2006) 97106.] proved global existence and uniform boundedness of the radial solutions when the L1-norm of the initial data satisfies a threshold condition. We prove in this letter that this result prescribes a region in the plane of masses which is sharp in the sense that if the drift-diffusion system is initiated outside the threshold region of global existence, then blow-up is possible: suitable initial data can be built up in such a way that the corresponding solution blows up in a finite time. © 2011 Elsevier Ltd. All rights reserved.
Conca, C., & Espejo, E. (2012). Threshold condition for global existence and blow-up to a radially symmetric drift-diffusion system. Applied Mathematics Letters, 25(3), 352–356. https://doi.org/10.1016/j.aml.2011.09.013