论文标题
在BESOV空间中的分数热半群和产品估计中，分数Keller-Segel系统的理论分析中的应用
On the fractional heat semigroup and product estimates in Besov spaces and applications in theoretical analysis of the fractional Keller-Segel system
论文作者
论文摘要
本文涉及时间和空间变量中的分数凯勒 - 塞格系统。我们考虑物理变量的分数耗散，包括用于趋化扩散的分数耗散机制，以及在Caputo意义上假定的时间分数变化。我们分析了关键空间中Mittag-Leffler操作员的时间衰减的分数热群和积分估计值，并证明了源自Keller-Segel System的非线性的双线性估计值，而无需使用辅助规范。我们使用这些结果来证明仅使用自然持久空间的规范，包括存在自相似的解决方案，这构成了该框架的持久性。此外，我们证明了唯一性结果，而没有假设初始数据的任何较小条件。
This paper is concerned with the fractional Keller-Segel system in the temporal and spatial variables. We consider fractional dissipation for the physical variables including a fractional dissipation mechanism for the chemotactic diffusion, as well as a time fractional variation assumed in the Caputo sense. We analyze the fractional heat semigroup obtaining time decay and integral estimates of the Mittag-Leffler operators in critical Besov spaces, and prove a bilinear estimate derived from the nonlinearity of the Keller-Segel system, without using auxiliary norms. We use these results in order to prove the existence of global solutions in critical homogeneous Besov spaces employing only the norm of the natural persistence space, including the existence of self-similar solutions, which constitutes a persistence result in this framework. In addition, we prove a uniqueness result without assuming any smallness condition of the initial data.
