THE GLOBAL EXISTENCE OF STRONG SOLUTIONS FOR A NON-ISOTHERMAL IDEAL GAS SYSTEM

doi:10.1007/s10473-024-0306-9

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (3): 865-886.doi: 10.1007/s10473-024-0306-9

THE GLOBAL EXISTENCE OF STRONG SOLUTIONS FOR A NON-ISOTHERMAL IDEAL GAS SYSTEM

Bin Han¹, Ningan Lai^2,*, Andrei Tarfulea³

1. Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China;
2. School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China;
3. Department of Mathematics, Louisiana State University, Baton Rouge 70803, USA

收稿日期:2022-12-02 修回日期:2023-01-08 出版日期:2024-06-25 发布日期:2024-05-21

THE GLOBAL EXISTENCE OF STRONG SOLUTIONS FOR A NON-ISOTHERMAL IDEAL GAS SYSTEM

Bin Han¹, Ningan Lai^2,*, Andrei Tarfulea³

1. Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China;
2. School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China;
3. Department of Mathematics, Louisiana State University, Baton Rouge 70803, USA

Received:2022-12-02 Revised:2023-01-08 Online:2024-06-25 Published:2024-05-21
Contact: *Ningan Lai, E-mail:ninganlai@zjnu.edu.cn
About author:Bin Han,E-mail:hanbin@hdu.edu.cn; Andrei Tarfulea, E-mail:tarfulea@lsu.edu
Supported by:
Zhejiang Province Science Fund (LY21A010009). The second author was partially supported by the National Science Foundation of China (12271487, 12171097). The third author was partially supported by the National Science Foundation (DMS-2012333, DMS-2108209).

摘要/Abstract

摘要： We investigate the global existence of strong solutions to a non-isothermal ideal gas model derived from an energy variational approach. We first show the global well-posedness in the Sobolev space $H^{2}\left(\mathbb{R}^{3}\right)$ for solutions near equilibrium through iterated energy-type bounds and a continuity argument. We then prove the global well-posedness in the critical Besov space $\dot{B}_{2,1}^{3 / 2}$ by showing that the linearized operator is a contraction mapping under the right circumstances.

关键词: thermal fluid equations, energy-variational method, well-posedness theory for PDE, paraproduct calculus

Abstract: We investigate the global existence of strong solutions to a non-isothermal ideal gas model derived from an energy variational approach. We first show the global well-posedness in the Sobolev space $H^{2}\left(\mathbb{R}^{3}\right)$ for solutions near equilibrium through iterated energy-type bounds and a continuity argument. We then prove the global well-posedness in the critical Besov space $\dot{B}_{2,1}^{3 / 2}$ by showing that the linearized operator is a contraction mapping under the right circumstances.

Key words: thermal fluid equations, energy-variational method, well-posedness theory for PDE, paraproduct calculus

中图分类号:

35A01

Bin Han, Ningan Lai, Andrei Tarfulea. THE GLOBAL EXISTENCE OF STRONG SOLUTIONS FOR A NON-ISOTHERMAL IDEAL GAS SYSTEM[J]. 数学物理学报(英文版), 2024, 44(3): 865-886.

Bin Han, Ningan Lai, Andrei Tarfulea. THE GLOBAL EXISTENCE OF STRONG SOLUTIONS FOR A NON-ISOTHERMAL IDEAL GAS SYSTEM[J]. Acta mathematica scientia,Series B, 2024, 44(3): 865-886.

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THE GLOBAL EXISTENCE OF STRONG SOLUTIONS FOR A NON-ISOTHERMAL IDEAL GAS SYSTEM

THE GLOBAL EXISTENCE OF STRONG SOLUTIONS FOR A NON-ISOTHERMAL IDEAL GAS SYSTEM

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