Beris-Edwards模型在三维空间中的整体适定性

基金项目:

国家自然科学基金项目(11371152)

详细信息

Global Well-Posedness for the Beris-Edwards System in Three-Dimensional Space

1.
（1.College of Mathematics and Statistics,Hanshan Normal University,Chaozhou 521041,China;
2.
2.School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China;
3.
3.School of Mathematics and Computational Science,Wuyi University,Jiangmen 529020,China)

摘要: 考虑了由Navier-Stokes方程组与Q张量抛物系统耦合所描述的一类Q张量动力学模型在三维空间中的Cauchy问题, 利用能量方法与经典的Friedrich方法证明了弱解的整体存在性,估计了大粘性系数条件下整体弱解的高阶正则性, 进而得到整体强解的存在性, 并得到了其弱强唯一性.
- Q-张量 /
- 向列型液晶 /
- 整体解 /
- 唯一性
Abstract: The Cauchy problem for a dynamical Q-tensor model which couples a forced Navier-Stokes equations with a parabolic-type Q-tensor system in three-dimensional space is considered. Firstly, the global existence of weak solutions is proved by energy method and classical Friedrich's method, and the higher regularity of the global weak solutions is estimated provided that the viscosity of the fluid is sufficiently large. Then, the global existence of strong solutions is established.Finally, a continuous dependence result on the initial data is also given.
- Q-tensor /
- nematic liquid crystals /
- global solutions /
- uniqueness