Abstract
The Cauchy problems for Keller–Segel system are studied using homogeneous Besov spaces. With the homogeneous Besov spaces B ˙ p , ∞ − 2 + n p ( R n ) , which is the scaling critical case for Keller–Segel system, global solutions for small initial data are obtained in the space. In addition, ill-posedness for Keller–Segel system is also studied.
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