Finite-time Singularities of an Aggregation Equation in R with Fractional Dissipation

نویسندگان

  • DONG LI
  • JOSE RODRIGO
چکیده

We consider an aggregation equation in Rn, n ≥ 2, with fractional dissipation, namely, ut + ∇ · (u∇K ∗ u) = −ν(−∆)γ/2u , where 0 ≤ γ ≤ 2 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 0 ≤ γ < 1 the solutions develop blow-up in finite for a general class of initial data. In contrast we prove that for 1 < γ ≤ 2 the equation is globally well-posed.

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تاریخ انتشار 2008