Global strong solutions and optimal $L^2$ decay to the compressible FENE dumbbell model

Abstract

In this paper, we are concerned with the global well-posedness and $L^2$ decay rate for the strong solutions of the compressible finite extensible nonlinear elastic (FENE) dumbbell model. For $d\ge 2$, we prove that the compressible FENE dumbbell model admits a unique global strong solution provided the initial data are close to equilibrium state. Moreover, by the Littlewood-Paley decomposition theory and the Fourier splitting method, we show optimal $L^2$ decay rate of global strong solutions for $d\ge 3$.

26 pages. arXiv admin note: substantial text overlap with arXiv:2104.10844

References in corpus (1)

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