A GLOBAL EXISTENCE RESULT FOR KORTEWEG SYSTEM IN THE CRITICAL LP FRAMEWORK

doi:10.1007/s10473-019-0614-7

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (6): 1639-1660.doi: 10.1007/s10473-019-0614-7

A GLOBAL EXISTENCE RESULT FOR KORTEWEG SYSTEM IN THE CRITICAL L^P FRAMEWORK

高真圣¹, 梁言¹, 谭忠²

1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China;
2. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

收稿日期:2018-05-02 修回日期:2019-01-26 出版日期:2019-12-25 发布日期:2019-12-30
通讯作者: Zhong TAN,E-mail:ztan85@163.com E-mail:ztan85@163.com
作者简介:Zhensheng GAO,E-mail:gaozhensheng@hqu.edu.cn;Yan LIANG,E-mail:yliang@hqu.edu.cn
基金资助:
Gao's research was supported by Natural Science Foundation of Fujian Province (JZ160406), Tan's research was partly supported by National Natural Science Foundation of China-NSAF (11271305 and 11531010).

A GLOBAL EXISTENCE RESULT FOR KORTEWEG SYSTEM IN THE CRITICAL L^P FRAMEWORK

Zhensheng GAO¹, Yan LIANG¹, Zhong TAN²

1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China;
2. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

Received:2018-05-02 Revised:2019-01-26 Online:2019-12-25 Published:2019-12-30
Contact: Zhong TAN,E-mail:ztan85@163.com E-mail:ztan85@163.com
Supported by:
Gao's research was supported by Natural Science Foundation of Fujian Province (JZ160406), Tan's research was partly supported by National Natural Science Foundation of China-NSAF (11271305 and 11531010).

摘要/Abstract

摘要： The purpose of this work is to investigate the initial value problem for a general isothermal model of capillary fluids derived by Dunn and Serrin[12], which can be used as a phase transition model. Motivated by[9], we aim at extending the work by Danchin-Desjardins[11] to a critical framework which is not related to the energy space. For small perturbations of a stable equilibrium state in the sense of suitable L^p-type Besov norms, we establish the global existence. As a consequence, like for incompressible flows, one may exhibit a class of large highly oscillating initial velocity fields for which global existence and uniqueness holds true.

关键词: Korteweg system, global existence, L^p-type Besov norms

Abstract: The purpose of this work is to investigate the initial value problem for a general isothermal model of capillary fluids derived by Dunn and Serrin[12], which can be used as a phase transition model. Motivated by[9], we aim at extending the work by Danchin-Desjardins[11] to a critical framework which is not related to the energy space. For small perturbations of a stable equilibrium state in the sense of suitable L^p-type Besov norms, we establish the global existence. As a consequence, like for incompressible flows, one may exhibit a class of large highly oscillating initial velocity fields for which global existence and uniqueness holds true.

Key words: Korteweg system, global existence, L^p-type Besov norms

中图分类号:

35B40

高真圣, 梁言, 谭忠. A GLOBAL EXISTENCE RESULT FOR KORTEWEG SYSTEM IN THE CRITICAL L^P FRAMEWORK[J]. 数学物理学报(英文版), 2019, 39(6): 1639-1660.

Zhensheng GAO, Yan LIANG, Zhong TAN. A GLOBAL EXISTENCE RESULT FOR KORTEWEG SYSTEM IN THE CRITICAL L^P FRAMEWORK[J]. Acta mathematica scientia,Series B, 2019, 39(6): 1639-1660.

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A GLOBAL EXISTENCE RESULT FOR KORTEWEG SYSTEM IN THE CRITICAL L^P FRAMEWORK

A GLOBAL EXISTENCE RESULT FOR KORTEWEG SYSTEM IN THE CRITICAL L^P FRAMEWORK

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