On the initial value problem for the hyperbolic Keller-Segel equations in Besov spaces
On the initial value problem for the hyperbolic Keller-Segel equations in Besov spaces
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DOI：
10.1016/j.jde.2022.06.026
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发表时间：
2022-10
影响因子：
2.4
通讯作者：
Lei Zhang;Chunlai Mu;Shouming Zhou
中科院分区：
文献类型：
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作者：
Lei Zhang;Chunlai Mu;Shouming Zhou
本文首先通过构造一个特殊的初值，证明了一维双曲型Keller-Segel方程（HKSE）从u 0出发的解映射在t= 0时在度量B 2，∞ s（R），s> 32中是不连续的.然后，我们在更大的Besov空间B p，1 1+ dp（Rd），1≤ p<∞中建立了高维HKSE的Hadamard局部适定性结果，改进了[Zhou，Zhang & Mu，J. Differ.方程式，302（2021），pp. 662-679]。此外，在与初始值相同的Besov空间拓扑中，研究了具有小扩散系数<$Δu的Keller-Segel方程在<$Δ → 0时的无粘极限.最后，我们利用Littlewood-Paley理论建立了Besov空间中强解的两类爆破准则。
In this paper, we first show by constructing a special initial data that the solution map for the one dimensional hyperbolic Keller-Segel equations (HKSE) starting from u 0 is discontinuous at t= 0 in the metric of B 2,∞ s (R), s> 3 2. Then, we establish the Hadamard local well-posedness result for the high dimensional HKSE in the larger Besov spaces B p, 1 1+ d p (R d), 1≤ p<∞, which improves the local theory proved by [Zhou, Zhang & Mu, J. Differ. Equ., 302 (2021), pp. 662-679]. Moreover, we investigate the inviscid limit of the Keller-Segel equations with small diffusivity ϵΔu as ϵ→ 0 in the same topology of Besov spaces as the initial data. Finally, we establish two kinds of blow-up criteria for strong solutions in Besov spaces by means of the Littlewood-Paley theory.