POINTWISE SPACE-TIME BEHAVIOR OF A COMPRESSIBLE NAVIER-STOKES-KORTEWEG SYSTEM IN DIMENSION THREE

doi:10.1007/s10473-022-0522-0

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (5): 2113-2130.doi: 10.1007/s10473-022-0522-0

• 论文 • 上一篇

POINTWISE SPACE-TIME BEHAVIOR OF A COMPRESSIBLE NAVIER-STOKES-KORTEWEG SYSTEM IN DIMENSION THREE

Xiaopan JIANG, Zhigang WU

Department of Mathematics, Donghua University, Shanghai, 201620, China

收稿日期:2020-06-15 修回日期:2022-05-27 发布日期:2022-11-02
通讯作者: Zhigang Wu,E-mail:zgwu@dhu.edu.cn E-mail:zgwu@dhu.edu.cn
基金资助:
Supported by Natural Science Foundation of China (11971100) and Natural Science Foundation of Shanghai (22ZR1402300).

POINTWISE SPACE-TIME BEHAVIOR OF A COMPRESSIBLE NAVIER-STOKES-KORTEWEG SYSTEM IN DIMENSION THREE

Xiaopan JIANG, Zhigang WU

Department of Mathematics, Donghua University, Shanghai, 201620, China

Received:2020-06-15 Revised:2022-05-27 Published:2022-11-02
Contact: Zhigang Wu,E-mail:zgwu@dhu.edu.cn E-mail:zgwu@dhu.edu.cn
Supported by:
Supported by Natural Science Foundation of China (11971100) and Natural Science Foundation of Shanghai (22ZR1402300).

摘要/Abstract

摘要： The Cauchy problem of compressible Navier-Stokes-Korteweg system in $\mathbb{R}^3$ is considered here. Due to capillarity effect of material, we obtain the pointwise estimates of the solution in an H⁴-framework, which is different from the previous results for the compressible Navier-Stokes system in an H⁶-framework [24, 25]. Our result mainly relies on two different descriptions of the singularity in the short wave of Green’s function for dealing initial propagation and nonlinear coupling respectively. Our pointwise results demonstrate the generalized Huygens’ principle as the compressible Navier-Stokes system. As a corollary, we have an L^p estimate of the solution with p > 1, which is a generalization for p ≥ 2 in [33].

关键词: Navier-Stokes-Korteweg system, Green’s function, Large time behavior

Abstract: The Cauchy problem of compressible Navier-Stokes-Korteweg system in $\mathbb{R}^3$ is considered here. Due to capillarity effect of material, we obtain the pointwise estimates of the solution in an H⁴-framework, which is different from the previous results for the compressible Navier-Stokes system in an H⁶-framework [24, 25]. Our result mainly relies on two different descriptions of the singularity in the short wave of Green’s function for dealing initial propagation and nonlinear coupling respectively. Our pointwise results demonstrate the generalized Huygens’ principle as the compressible Navier-Stokes system. As a corollary, we have an L^p estimate of the solution with p > 1, which is a generalization for p ≥ 2 in [33].

Key words: Navier-Stokes-Korteweg system, Green’s function, Large time behavior

中图分类号:

35B40

Xiaopan JIANG, Zhigang WU. POINTWISE SPACE-TIME BEHAVIOR OF A COMPRESSIBLE NAVIER-STOKES-KORTEWEG SYSTEM IN DIMENSION THREE[J]. 数学物理学报(英文版), 2022, 42(5): 2113-2130.

Xiaopan JIANG, Zhigang WU. POINTWISE SPACE-TIME BEHAVIOR OF A COMPRESSIBLE NAVIER-STOKES-KORTEWEG SYSTEM IN DIMENSION THREE[J]. Acta mathematica scientia,Series B, 2022, 42(5): 2113-2130.

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POINTWISE SPACE-TIME BEHAVIOR OF A COMPRESSIBLE NAVIER-STOKES-KORTEWEG SYSTEM IN DIMENSION THREE

POINTWISE SPACE-TIME BEHAVIOR OF A COMPRESSIBLE NAVIER-STOKES-KORTEWEG SYSTEM IN DIMENSION THREE

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