GLOBAL WEAK SOLUTIONS OF COMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ-MAXWELL EQUATIONS FOR QUANTUM FLUIDS IN DIMENSION THREE*

doi:10.1007/s10473-023-0102-y

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (1): 25-42.doi: 10.1007/s10473-023-0102-y

GLOBAL WEAK SOLUTIONS OF COMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ-MAXWELL EQUATIONS FOR QUANTUM FLUIDS IN DIMENSION THREE^*

Quansen Jiu, Lin Ma^†

School of Mathematical Sciences, Capital Normal University, Beijing 100048, China

收稿日期:2021-09-29 修回日期:2022-06-21 发布日期:2023-03-01
通讯作者: †Lin MA. E-mail: malin.cnu@foxmail.com
基金资助:
*National Natural Sciences Foundation of China (11931010, 12061003).

GLOBAL WEAK SOLUTIONS OF COMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ-MAXWELL EQUATIONS FOR QUANTUM FLUIDS IN DIMENSION THREE^*

Quansen Jiu, Lin Ma^†

School of Mathematical Sciences, Capital Normal University, Beijing 100048, China

Received:2021-09-29 Revised:2022-06-21 Published:2023-03-01
Contact: †Lin MA. E-mail: malin.cnu@foxmail.com
About author:Quansen Jiu, jiuqs@cnu.edu.cn
Supported by:
*National Natural Sciences Foundation of China (11931010, 12061003).

摘要/Abstract

摘要： In this paper, we consider the weak solutions of compressible Navier-Stokes-Landau-Lifshitz-Maxwell (CNSLLM) system for quantum fluids with a linear density dependent viscosity in a 3D torus. By introducing the cold pressure $P_c$, we prove the global existence of weak solutions with the pressure $P+P_c$, where $P = A \rho^{\gamma}$ with $\gamma\ge1$. Our main result extends the one in [13] on the quantum Navier-Stokes equations to the CNSLLM system.

关键词: compressible Navier-Stokes-Landau-Lifshitz-Maxwell equations, global existence, weak solutions, quantum fluid

Abstract: In this paper, we consider the weak solutions of compressible Navier-Stokes-Landau-Lifshitz-Maxwell (CNSLLM) system for quantum fluids with a linear density dependent viscosity in a 3D torus. By introducing the cold pressure $P_c$, we prove the global existence of weak solutions with the pressure $P+P_c$, where $P = A \rho^{\gamma}$ with $\gamma\ge1$. Our main result extends the one in [13] on the quantum Navier-Stokes equations to the CNSLLM system.

Key words: compressible Navier-Stokes-Landau-Lifshitz-Maxwell equations, global existence, weak solutions, quantum fluid

Quansen Jiu, Lin Ma. GLOBAL WEAK SOLUTIONS OF COMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ-MAXWELL EQUATIONS FOR QUANTUM FLUIDS IN DIMENSION THREE^*[J]. 数学物理学报(英文版), 2023, 43(1): 25-42.

Quansen Jiu, Lin Ma. GLOBAL WEAK SOLUTIONS OF COMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ-MAXWELL EQUATIONS FOR QUANTUM FLUIDS IN DIMENSION THREE^*[J]. Acta mathematica scientia,Series B, 2023, 43(1): 25-42.

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GLOBAL WEAK SOLUTIONS OF COMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ-MAXWELL EQUATIONS FOR QUANTUM FLUIDS IN DIMENSION THREE^*

GLOBAL WEAK SOLUTIONS OF COMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ-MAXWELL EQUATIONS FOR QUANTUM FLUIDS IN DIMENSION THREE^*

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