REMARKS ON THE GLOBAL EXISTENCE OF WEAK SOLUTIONS TO QUASILINEAR DEGENERATE KELLER-SEGEL SYSTEMS

摘要

The global existence of weak solutions to quasilinear "degenerate" Keller-Segel systems is shown in the recent papers [3], [4]. This paper gives some improvements and supplements of these. More precisely, the differentiability and the smallness of initial data are weakened when the spatial dimension N satisfies N ≥ 2. Moreover, the global existence is established in the case N = 1 which is unsolved in [4].