$\mathbb{R}^2$ 中双轴向列相的框架流体力学全局弱解的唯一性

IF 1.2 4区 数学 Q2 MATHEMATICS, APPLIED
Sirui Li, Chenchen Wang, Jie Xu
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引用次数: 0

摘要

我们考虑了由正交框架场描述的双轴向列相的流体力学,该正交框架场可从基于分子理论的张量模型中导出。我们证明了二维框架流体力学 Cauchy 问题全局弱解的唯一性。证明主要基于 Littlewood-Paley 分析中合适的弱能量估计。我们充分利用了$SO(3)$上带有旋转导数的非线性项的估计,以及双轴框架系统的抵消关系和耗散结构。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Uniqueness of global weak solutions to the frame hydrodynamics for biaxial nematic phases in $\mathbb{R}^2$
We consider the hydrodynamics for biaxial nematic phases described by a field of orthonormal frame, which can be derived from a molecular-theory-based tensor model. We prove the uniqueness of global weak solutions to the Cauchy problem of the frame hydrodynamics in dimension two. The proof is mainly based on the suitable weaker energy estimates within the Littlewood–Paley analysis. We take full advantage of the estimates of nonlinear terms with rotational derivatives on $SO(3)$, together with cancellation relations and dissipative structures of the biaxial frame system.
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来源期刊
CiteScore
1.70
自引率
10.00%
发文量
59
审稿时长
6 months
期刊介绍: Covers modern applied mathematics in the fields of modeling, applied and stochastic analyses and numerical computations—on problems that arise in physical, biological, engineering, and financial applications. The journal publishes high-quality, original research articles, reviews, and expository papers.
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