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2024 | OriginalPaper | Chapter

The Ericksen-Leslie System for Data on a Plane

Authors : Daniele Barbera, Vladimir Georgiev

Published in: New Trends in the Applications of Differential Equations in Sciences

Publisher: Springer Nature Switzerland

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Abstract

The work deals with the Ericksen-Leslie system for nematic liquid crystals on the whole space with dimension greater or equal than 3. In our work we suppose the initial condition of the orientation field 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 with decay in time for small initial data of a solution in Sobolev spaces asking low regularity for the initial conditions.

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previous chapter Robin Boundary Value Problem for Some Nonlinear Nonlocal Elliptic Partial Differential Equations

next chapter High Frequency Weighted Resolvent Estimates for the Dirichlet Laplacian in the Exterior Domain

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Title: The Ericksen-Leslie System for Data on a Plane
Authors: Daniele Barbera
Vladimir Georgiev
Publisher: Springer Nature Switzerland
Book: New Trends in the Applications of Differential Equations in Sciences
Print ISBN: 978-3-031-53211-5

Electronic ISBN: 978-3-031-53212-2

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-53212-2_8

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