GLOBAL SOLUTIONS TO THE 2D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH SOME LARGE INITIAL DATA*

doi:10.1007/s10473-023-0315-0

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (3): 1251-1274.doi: 10.1007/s10473-023-0315-0

GLOBAL SOLUTIONS TO THE 2D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH SOME LARGE INITIAL DATA^*

Xiaoping Zhai¹, Xin Zhong^2,†

1. School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510520, China;
2. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

收稿日期:2021-12-21 接受日期:2022-10-17 出版日期:2023-06-25 发布日期:2023-06-06
通讯作者: ^† Xin Zhong, E-mail: xzhong1014@amss.ac.cn
作者简介:Xiaoping Zhai, E-mail: pingxiaozhai@163.com
基金资助:
Zhai was partially supported by the Guangdong Provincial Natural Science Foundation (2022A1515011977) and the Science and Technology Program of Shenzhen (20200806104726001). Zhong was partially supported by the NNSF of China (11901474, 12071359) and the Exceptional Young Talents Project of Chongqing Talent (cstc2021ycjh-bgzxm0153).

GLOBAL SOLUTIONS TO THE 2D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH SOME LARGE INITIAL DATA^*

Xiaoping Zhai¹, Xin Zhong^2,†

1. School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510520, China;
2. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Received:2021-12-21 Accepted:2022-10-17 Online:2023-06-25 Published:2023-06-06
Contact: ^† Xin Zhong, E-mail: xzhong1014@amss.ac.cn
About author:Xiaoping Zhai, E-mail: pingxiaozhai@163.com
Supported by:
Zhai was partially supported by the Guangdong Provincial Natural Science Foundation (2022A1515011977) and the Science and Technology Program of Shenzhen (20200806104726001). Zhong was partially supported by the NNSF of China (11901474, 12071359) and the Exceptional Young Talents Project of Chongqing Talent (cstc2021ycjh-bgzxm0153).

摘要/Abstract

摘要： We consider the global well-posedness of strong solutions to the Cauchy problem of compressible barotropic Navier-Stokes equations in $\mathbb{R}^2$. By exploiting the global-in-time estimate to the two-dimensional (2D for short) classical incompressible Navier-Stokes equations and using techniques developed in (SIAM J Math Anal, 2020, 52(2): 1806-1843), we derive the global existence of solutions provided that the initial data satisfies some smallness condition. In particular, the initial velocity with some arbitrary Besov norm of potential part $\mathbb{P} u_0$ and large high oscillation are allowed in our results. Moreover, we also construct an example with the initial data involving such a smallness condition, but with a norm that is arbitrarily large.

关键词: compressible Navier-Stokes equations, global large solutions, Littlewood-Paley theory

Abstract: We consider the global well-posedness of strong solutions to the Cauchy problem of compressible barotropic Navier-Stokes equations in $\mathbb{R}^2$. By exploiting the global-in-time estimate to the two-dimensional (2D for short) classical incompressible Navier-Stokes equations and using techniques developed in (SIAM J Math Anal, 2020, 52(2): 1806-1843), we derive the global existence of solutions provided that the initial data satisfies some smallness condition. In particular, the initial velocity with some arbitrary Besov norm of potential part $\mathbb{P} u_0$ and large high oscillation are allowed in our results. Moreover, we also construct an example with the initial data involving such a smallness condition, but with a norm that is arbitrarily large.

Key words: compressible Navier-Stokes equations, global large solutions, Littlewood-Paley theory

Xiaoping Zhai, Xin Zhong. GLOBAL SOLUTIONS TO THE 2D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH SOME LARGE INITIAL DATA^*[J]. 数学物理学报(英文版), 2023, 43(3): 1251-1274.

Xiaoping Zhai, Xin Zhong. GLOBAL SOLUTIONS TO THE 2D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH SOME LARGE INITIAL DATA^*[J]. Acta mathematica scientia,Series B, 2023, 43(3): 1251-1274.

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GLOBAL SOLUTIONS TO THE 2D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH SOME LARGE INITIAL DATA^*

GLOBAL SOLUTIONS TO THE 2D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH SOME LARGE INITIAL DATA^*

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