一类时滞非牛顿流体在二维无界域上的适定性

数学物理学报 ›› 2023, Vol. 43 ›› Issue (6): 1789-1802.

一类时滞非牛顿流体在二维无界域上的适定性

刘国威^*(),王启玲()

重庆师范大学数学科学学院重庆 401331

收稿日期:2022-11-07 修回日期:2023-03-02 出版日期:2023-12-26 发布日期:2023-11-16
通讯作者: *刘国威，E-mail: guoweiliu@cqnu.edu.cn
作者简介:王启玲，E-mail: 2690803827@qq.com
基金资助:
国家自然科学基金(12001073);重庆市自然科学基金(cstc2020jcyj-msxmX0709);重庆市教育委员会科学技术研究基金(KJQN201900563)

The Well-posedness of a Delayed Non-Newtonian Fluid on ${2D}$ Unbounded Domains

Liu Guowei^*(),Wang Qiling()

School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331

Received:2022-11-07 Revised:2023-03-02 Online:2023-12-26 Published:2023-11-16
Supported by:
NSFC(12001073);NSF of Chongqing(cstc2020jcyj-msxmX0709);Science and Technology Research Foundation of Chongqing Education Commission(KJQN201900563)

摘要/Abstract

摘要：

该文研究了一类非自治的时滞不可压缩非牛顿流体在二维无界区域上的整体适定性. 在外力项具有最低正则性时, 该文结合空间区域分解技术和 Garlekin 方法建立了解的存在性, 然后利用能量估计的方法得到了解的唯一性和稳定性.

关键词: 非牛顿流体, 时滞, 适定性

Abstract:

In this paper, we study the well-poseness of a non-autonomous delayed incompressible non-Newtonian fluid on $2D$ unbounded domains. With a minimal regularity of the force, we prove the existence of solutions by the method of combining the technique of domain decomposition with the Garlerin approximation. Then we use the energy method to prove the uniqueness and the stability of solutions.

Key words: Non-Newtonian fluid, Delay, Well-posedness

中图分类号:

O373

刘国威, 王启玲. 一类时滞非牛顿流体在二维无界域上的适定性[J]. 数学物理学报, 2023, 43(6): 1789-1802.

Liu Guowei, Wang Qiling. The Well-posedness of a Delayed Non-Newtonian Fluid on ${2D}$ Unbounded Domains[J]. Acta mathematica scientia,Series A, 2023, 43(6): 1789-1802.

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