Asymptotics of Chemotaxis Systems with Fractional Dissipation for Small Data in Critical Sobolev Space

Abstract

A chemotaxis system with Newtonian attraction and fractional dissipation of order alpha is an element of (0, 2) is considered in R-N. For initial data belonging to L-1 boolean AND H-4 but small in L-N/alpha, N = 2, 3, the temporal decay and the asymptotic behavior of a global classical solution are established. In particular, we derive a precise decay estimate for higher Sobolev norms.