arXiv subjects

Zhaonan Luo

Publications and source records attributed to Zhaonan Luo.

22 records · Page 2Linked to original sources

arXiv2021

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

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.

math.AP↗

arXiv2021

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

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 $d\geq 2$, 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 $d\geq 3$.

math.AP↗

arXiv2020

Large time behavior to the FENE dumbbell model of polymeric flows near equilibrium

In this paper we mainly study large time behavior for the strong solutions of the finite extensible nonlinear elastic (FENE) dumbbell model. There is a lot results about the $L^2$ decay rate of the co-rotation model. In this paper, we consider the general case. We prove that the optimal $L^2$ decay rate of the velocity is $(1+t)^{-\frac{d}{4}}$ with $d\geq 2$. This result improves the previous result in \cite{Luo-Yin}.

math.AP↗

arXiv2020

Vanishing viscosity limit to the FENE dumbbell model of polymeric flows

In this paper we mainly investigate the inviscid limit for the strong solutions of the finite extensible nonlinear elastic (FENE) dumbbell model. By virtue of the Littlewood-Paley theory, we first obtain a uniform estimate for the solution to the FENE dumbbell model with viscosity in Besov spaces. Moreover, we show that the data-to-solution map is continuous. Finally, we prove that the strong solution of the FENE dumbbell model converges to a Euler system couple with a Fokker-Planck equation. Furthermore, convergence rates in Lebesgue spaces are obtained also.

math.AP↗