Estimates on the Laplace Operator in Heat Flows of Harmonic Maps

Qingtong Wu

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arXiv · 2410.20419

Estimates on the Laplace Operator in Heat Flows of Harmonic Maps

Qingtong Wu

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Abstract

In this paper we investigate estimates about the Laplace operator in heat flows of harmonic maps, focusing outside the singularities through spherical coordinates. These estimates can be used in the general Ericksen--Leslie system to obtain higher-order estimates. We consider the problem subject to the $\mathbb{T}^2$ and $\mathbb{T}^3$ boundary conditions.

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Qingtong Wu. 2024-10-27. Estimates on the Laplace Operator in Heat Flows of Harmonic Maps. https://arxiv.org/abs/2410.20419

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