Global regularity and optimal decay estimates of large solutions to the compressible FENE system

2024/08/02 by Zhaonan Luo, Luo, Zhaonan, Zhiying Meng +3
Mathematics · Engineering · #Advanced Mathematical Physics Problems #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2408.00993

Abstract

In this paper, we are concerned with the compressible FENE dumbbell model. By virtue of the dissipative structure and the interpolation method, we firstly prove global regularity in H² framework for the compressible FENE system with some large data. Then, we obtain optimal decay estimates of large solutions in H¹ and remove the smallness assumption of low frequencies by virtue of the Fourier splitting method and the Littlewood-Paley decomposition theory. Furthermore, we establish optimal decay rate for the highest derivative of the solutions by a different method combining time frequency decomposition and the time weighted energy estimate. These obtained results generalize and cover the classical results of the incompressible FENE dumbbell model.

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