On $ L^p $ estimates for a simplified Ericksen-Leslie system

Jinrui Huang; Wenjun Wang; Huanyao Wen

doi:10.3934/cpaa.2020075

Article Contents

2020, Volume 19, Issue 3: 1485-1507. Doi: 10.3934/cpaa.2020075

This issue Previous Article Fredholm theory for an elliptic differential operator defined on

$ \mathbb{R}^n $

and acting on generalized Sobolev spaces Next Article Unique strong solutions and V-attractor of a three dimensional globally modified magnetohydrodynamic equations

On $ L^p $ estimates for a simplified Ericksen-Leslie system

1.
School of Mathematics and Computational Science, Wuyi University, Jiangmen 529020, China
2.
College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
3.
School of Mathematics, South China University of Technology, Guangzhou 510641, China

^* Corresponding author
^* Corresponding author

Received: April 30, 2019

Revised: July 31, 2019

Published: February 2020

J.R. Huang is partially supported by the National Natural Science Foundation of China (Grant Nos. 11971357, 11871005, 11771155 and 11571117), and by the Natural Science Foundation of Guangdong Province (Grant No. 2019A1515011491). W.J. Wang is partially supported by the National Natural Science Foundation of China (Grant No. 11871341). H.Y. Wen is partially supported by the National Natural Science Foundation of China (Grant Nos. 11671150, 11722104), and by GDUPS (2016)

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Abstract

In this paper, we study Cauchy problem for a simplified Ericksen-Leslie system in three dimensions. With the initial data of small perturbation near a steady state in $ H^2 $ norm, we obtain the global well-posedness of strong solutions as well as the $ L^p(p\in[1, 6]) $ estimates. In addition, sharper decay rates for the density and the momentum are obtained.

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Mathematics Subject Classification: Primary: 76N10, 74H40; Secondary: 76A15, 35Q30, 53C35.

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