Critical space for the parabolic-parabolic Keller–Segel model in Rd
Critical space for the parabolic-parabolic Keller–Segel model in Rd
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DOI：
10.1016/j.crma.2006.03.008
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发表时间：
2006-05
影响因子：
0.8
通讯作者：
L. Corrias;B. Perthame
中科院分区：
文献类型：
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作者：
L. Corrias;B. Perthame
研究了Rd中的Keller-Segel系统，当化学引诱剂浓度为抛物型方程时.证明了与椭圆情形类似的临界空间是初始细菌密度满足n 0 ∈ La（Rd），a> d/2，化学引诱剂浓度满足λ c 0 ∈ Ld（Rd）.在这些空间中，我们证明了小的初始数据产生的整体解决方案，消失的热方程为大的时间，并表现出正则化效果的超收缩型。引用这篇文章：L。科里亚斯，B。Perthame，CR Acad. Sci.巴黎，系列I 342（2006）。
We study the Keller–Segel system in Rd when the chemoattractant concentration is described by a parabolic equation. We prove that the critical space, with some similarity to the elliptic case, is that the initial bacteria density satisfies n0∈ La (Rd), a> d/2, and that the chemoattractant concentration satisfies∇ c0∈ Ld (Rd). In these spaces, we prove that small initial data give rise to global solutions that vanish as the heat equation for large times and that exhibit a regularizing effect of hypercontractivity type. To cite this article: L. Corrias, B. Perthame, CR Acad. Sci. Paris, Ser. I 342 (2006).