On parabolic partial differential equations with Hölder continuous diffusion coefficients

We investigate existence and regularity of weak solutions of a 1-dimensional parabolic differential equation with a non-constant H\"older diffusion coefficient and a rough forcing term. Such an equation appears in studying the 1-dimensional Ericksen-Leslie model for nematic liquid crystals wher...

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Bibliographic Details
Published in:arXiv.org 2023-01
Main Author: Sofiani, Majed
Format: Article
Language:English
Subjects:
Diffusion coefficient
Liquid crystals
Nematic crystals
Parabolic differential equations
Partial differential equations
Online Access:Get full text
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Summary:We investigate existence and regularity of weak solutions of a 1-dimensional parabolic differential equation with a non-constant H\"older diffusion coefficient and a rough forcing term. Such an equation appears in studying the 1-dimensional Ericksen-Leslie model for nematic liquid crystals where our result applies. The result presented here uses the H\"older continuity of the diffusion coefficient which comes from the physical background and the analysis of the Ericksen-Leslie model. Moreover, the dependence of the H\"older exponent of the solution is explicit on the H\"older exponent of the diffusion coefficient.
ISSN:2331-8422