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 $l\in \mathbb{N}$. By virtue of the time weighted energy estimate, we can improve the decay rate to $(1+t{)}^{-\frac{1}{4}}$. 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.

22 pages. arXiv admin note: substantial text overlap with arXiv:2107.08646, arXiv:2104.10844

References in corpus (1)

• Vanishing of vacuum states and blow-up phenomena of the compressible Navier-Stokes equations