数学物理学报 ›› 2019, Vol. 39 ›› Issue (5): 1125-1135.

• 论文 • 上一篇    

带有分数阶耗散的三维广义Oldroyd-B模型的整体正则性

张秋月   

  1. 河南理工大学数学与信息科学学院 河南焦作 454000
  • 收稿日期:2018-07-20 修回日期:2018-12-24 发布日期:2019-11-08
  • 通讯作者: 张秋月 E-mail:qyzhang0722@163.com

Global Regularity for 3D Generalized Oldroyd-B Type Models with Fractional Dissipation

Zhang Qiuyue   

  1. School of Mathematics and Information Science, Henan Polytechnic University, Henan Jiaozuo 454000
  • Received:2018-07-20 Revised:2018-12-24 Published:2019-11-08

摘要: 该文考虑了三维共旋情形下,带有分数阶耗散(-△)η1u和(-△)η2τ的广义不可压缩Oldroyd-B模型.假设初始数据(u0τ0)充分光滑,若耗散指标η1 ≥ 5/4,η2 ≥ 5/4,利用能量方法,得到了方程组经典解的整体正则性.

关键词: Oldroyd-B模型, 分数阶Laplace耗散, 整体正则性

Abstract: In this paper, we consider the 3D generalized Oldroyd-B type models with fractional Laplacian dissipation (-△)η1u and (-△)η2τ in the corotational case. By using energy method, for η1 ≥ 5/4 and η2 ≥ 5/4, we obtain the global regularity of classical solutions when the initial data (u0,τ0) are sufficiently smooth.

Key words: Oldroyd-B type models, Fractional Laplacian dissipation, Global regularity

中图分类号: 

  • O175.29