GLOBAL WELL-POSEDNESS AND OPTIMAL TIME DECAY RATES FOR THE GENERALIZED PHAN-THIEN-TANNER MODEL IN ${\mathbb{R}}^{3}$*

doi:10.1007/s10473-023-0317-y

Abstract

Abstract: In this paper, we consider the initial value problem for the incompressible generalized Phan-Thien-Tanner (GPTT) model. This model pertains to the dynamic properties of polymeric fluids. Under appropriate assumptions on smooth function $f$, we find a particular solution to the GPTT model. In dimension three, we establish the global existence and the optimal time decay rates of strong solutions provided that the initial data is close to the particular solution. The results which are presented here are generalizations of the network viscoelastic models.

Key words: viscoelastic fluids, global well-posedness, decay rates

Yuhui Chen, Qinghe Yao, Minling Li, Zheng-an Yao. GLOBAL WELL-POSEDNESS AND OPTIMAL TIME DECAY RATES FOR THE GENERALIZED PHAN-THIEN-TANNER MODEL IN ${\mathbb{R}}^{3}$^*[J].Acta mathematica scientia,Series B, 2023, 43(3): 1301-1322.

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References

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GLOBAL WELL-POSEDNESS AND OPTIMAL TIME DECAY RATES FOR THE GENERALIZED PHAN-THIEN-TANNER MODEL IN ${\mathbb{R}}^{3}$^*

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