Finite-Time Singularities of an Aggregation Equation in $${\mathbb {R}^n}$$ with Fractional Dissipation期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Finite-Time Singularities of an Aggregation Equation in $${\mathbb {R}^n}$$ with Fractional Dissipation

Authors:	Dong Li and Jose Rodrigo

Institution:	(1) School of Mathematics, Institute For Advanced Studies, Einstein Drive, Princeton, NJ 08540, USA;(2) Warwick University, Coventry, CV4 7AL, UK

Abstract:	We consider an aggregation equation in ${\mathbb {R}^n}$ , n ≥ 2 with fractional dissipation, namely, ${u_t + \nabla\cdot(u \nabla K*u)=-\nu (-\Delta)^{\gamma/2} u}$ , where 0 ≤ γ < 1 and K is a nonnegative decreasing radial kernel with a Lipschitz point at the origin, e.g. K(x) = e ^−\|x\|. We prove that for a class of smooth initial data, the solutions develop blow-up in finite time.

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