THE GLOBAL EXISTENCE AND A DECAY ESTIMATE OF SOLUTIONS TO THE PHAN-THEIN-TANNER MODEL

doi:10.1007/s10473-022-0314-6

数学物理学报 ›› 2022, Vol. 42 ›› Issue (3): 1058-1080.doi: 10.1007/s10473-022-0314-6

THE GLOBAL EXISTENCE AND A DECAY ESTIMATE OF SOLUTIONS TO THE PHAN-THEIN-TANNER MODEL

位瑞英¹, 李银², 姚正安³

1. School of Mathematics and Statistics, Shaoguan University, Shaoguan, 512005, China;
2. Faculty of Education, Shaoguan University, Shaoguan, 512005, China;
3. Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China

收稿日期:2020-10-03 修回日期:2021-07-04 出版日期:2022-06-26 发布日期:2022-06-24
通讯作者: Yin LI,E-mail:liyin2009521@163.com E-mail:liyin2009521@163.com
基金资助:
This work is partially supported by the National Natural Science Foundation of China (11926354, 11971496), Natural Science Foundation of Guangdong Province (2019A1515011320, 2021A1515010292, 2214050001249), Innovative team project of ordinary universities of Guangdong Province (2020KCXTD024), Characteristic innovation projects of ordinary colleges and universities in Guangdong Province (2020KTSCX134), and the Education Research Platform Project of Guangdong Province (2018179).

THE GLOBAL EXISTENCE AND A DECAY ESTIMATE OF SOLUTIONS TO THE PHAN-THEIN-TANNER MODEL

Ruiying WEI¹, Yin LI², Zheng-an YAO³

1. School of Mathematics and Statistics, Shaoguan University, Shaoguan, 512005, China;
2. Faculty of Education, Shaoguan University, Shaoguan, 512005, China;
3. Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China

Received:2020-10-03 Revised:2021-07-04 Online:2022-06-26 Published:2022-06-24
Contact: Yin LI,E-mail:liyin2009521@163.com E-mail:liyin2009521@163.com
Supported by:
This work is partially supported by the National Natural Science Foundation of China (11926354, 11971496), Natural Science Foundation of Guangdong Province (2019A1515011320, 2021A1515010292, 2214050001249), Innovative team project of ordinary universities of Guangdong Province (2020KCXTD024), Characteristic innovation projects of ordinary colleges and universities in Guangdong Province (2020KTSCX134), and the Education Research Platform Project of Guangdong Province (2018179).

摘要/Abstract

摘要： In this paper, we study the global existence and decay rates of strong solutions to the three dimensional compressible Phan-Thein-Tanner model. By a refined energy method, we prove the global existence under the assumption that the $H^3$ norm of the initial data is small, but that the higher order derivatives can be large. If the initial data belong to homogeneous Sobolev spaces or homogeneous Besov spaces, we obtain the time decay rates of the solution and its higher order spatial derivatives. Moreover, we also obtain the usual $L^p-L^2(1\leq p\leq2)$ type of the decay rate without requiring that the $L^p$ norm of initial data is small.

关键词: Phan-Thein-Tanner model, global existence, time decay rates

Abstract: In this paper, we study the global existence and decay rates of strong solutions to the three dimensional compressible Phan-Thein-Tanner model. By a refined energy method, we prove the global existence under the assumption that the $H^3$ norm of the initial data is small, but that the higher order derivatives can be large. If the initial data belong to homogeneous Sobolev spaces or homogeneous Besov spaces, we obtain the time decay rates of the solution and its higher order spatial derivatives. Moreover, we also obtain the usual $L^p-L^2(1\leq p\leq2)$ type of the decay rate without requiring that the $L^p$ norm of initial data is small.

Key words: Phan-Thein-Tanner model, global existence, time decay rates

中图分类号:

35Q30

位瑞英, 李银, 姚正安. THE GLOBAL EXISTENCE AND A DECAY ESTIMATE OF SOLUTIONS TO THE PHAN-THEIN-TANNER MODEL[J]. 数学物理学报, 2022, 42(3): 1058-1080.

Ruiying WEI, Yin LI, Zheng-an YAO. THE GLOBAL EXISTENCE AND A DECAY ESTIMATE OF SOLUTIONS TO THE PHAN-THEIN-TANNER MODEL[J]. Acta mathematica scientia,Series A, 2022, 42(3): 1058-1080.

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THE GLOBAL EXISTENCE AND A DECAY ESTIMATE OF SOLUTIONS TO THE PHAN-THEIN-TANNER MODEL

THE GLOBAL EXISTENCE AND A DECAY ESTIMATE OF SOLUTIONS TO THE PHAN-THEIN-TANNER MODEL

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