RN$\mathbb {R}^N$ 中埃里克森-莱斯利问题弧上的局部和全局解

IF 0.8 3区数学 Q2 MATHEMATICS Mathematische Nachrichten Pub Date : 2024-07-29 DOI:10.1002/mana.202300253

Daniele Barbera, Vladimir Georgiev

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引用次数: 0

摘要

我们的研究涉及有......空间的向列液晶的埃里克森-莱斯利系统。在我们的研究中，我们假设初始条件停留在连接单位球面上两个固定正交向量的弧线上。得益于这一几何假设，我们通过能量先验估计证明了在小初始数据条件下，Ⅳ 的解的局部存在性和全局存在性。

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Local and global solutions on arcs for the Ericksen–Leslie problem in R N $\mathbb {R}^N$

The work deals with the Ericksen–Leslie system for nematic liquid crystals on the space $R^{N}$ with $N \geq 3$ . In our work, we suppose the initial condition $v_{0}$ stays on an arc connecting two fixed orthogonal vectors on the unit sphere. Thanks to this geometric assumption, we prove through energy a priori estimates the local existence and the global existence for small initial data of a solution

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来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index

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