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

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

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

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

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

GLOBAL WELL-POSEDNESS AND OPTIMAL TIME DECAY RATES FOR THE GENERALIZED PHAN-THIEN-TANNER MODEL IN RR3{\mathbb{R}}^{3}*

GLOBAL WELL-POSEDNESS AND OPTIMAL TIME DECAY RATES FOR THE GENERALIZED PHAN-THIEN-TANNER MODEL IN RR3{\mathbb{R}}^{3}*

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

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

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doi:10.1007/s10473-023-0317-y

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (3): 1301-1322.doi: 10.1007/s10473-023-0317-y

Yuhui Chen¹, Qinghe Yao¹, Minling Li^2,†, Zheng-an Yao²

1. School of Aeronautics and Astronautics, Sun Yat-sen University, Guangzhou 510275, China;
2. School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China

收稿日期:2022-02-11 修回日期:2022-06-10 出版日期:2023-06-25 发布日期:2023-06-06
通讯作者: ^† Minling Li, E-mail: limling3@mail2.sysu.edu.cn
作者简介:Yuhui Chen, E-mail: chenyh339@mail.sysu.edu.cn; Qinghe Yao, E-mail: yaoqhe@mail.sysu.edu.cn;Zheng-an Yao,E-mail: mcsyao@mail.sysu.edu.cn
基金资助:
Yuhui Chen was supported by the NNSF of China (12201655); Qinghe Yao was supported by the NNSF of China (11972384) and the Guangdong Science and Technology Fund (2021B1515310001); Zheng-an Yao was supported by the NNSF of China (11971496) and the National Key R&D Program of China (2020YFA0712500).

Yuhui Chen¹, Qinghe Yao¹, Minling Li^2,†, Zheng-an Yao²

1. School of Aeronautics and Astronautics, Sun Yat-sen University, Guangzhou 510275, China;
2. School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China

Received:2022-02-11 Revised:2022-06-10 Online:2023-06-25 Published:2023-06-06
Contact: ^† Minling Li, E-mail: limling3@mail2.sysu.edu.cn
About author:Yuhui Chen, E-mail: chenyh339@mail.sysu.edu.cn; Qinghe Yao, E-mail: yaoqhe@mail.sysu.edu.cn;Zheng-an Yao,E-mail: mcsyao@mail.sysu.edu.cn
Supported by:
Yuhui Chen was supported by the NNSF of China (12201655); Qinghe Yao was supported by the NNSF of China (11972384) and the Guangdong Science and Technology Fund (2021B1515310001); Zheng-an Yao was supported by the NNSF of China (11971496) and the National Key R&D Program of China (2020YFA0712500).

摘要： 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.

关键词: viscoelastic fluids, global well-posedness, decay rates

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]. 数学物理学报(英文版), 2023, 43(3): 1301-1322.

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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