Large time behavior of global strong solutions to the 2-D compressible FENE dumbbell model

Abstract

In this paper, we mainly study large time behavior of the strong solutions to the 2-D compressible finite extensible nonlinear elastic (FENE) dumbbell model. The Fourier splitting method yields that the L 2 decay rate is ln −l (e + t) for any l ∈ N. By virtue of the time weighted energy estimate, we can improve the decay rate to (1 + t) − 1 4 . Under the low-frequency condition and by the Littlewood-Paley theory, we show that the solutions belong to some Besov space with negative index and obtain the optimal L 2 decay rate.