The Cauchy problem for the liquid crystals system in the critical Besov space with negative index

Sen Ming; Han Yang; Zili Chen; Ls Yong

Czechoslovak Mathematical Journal (2017)

  • Volume: 67, Issue: 1, page 37-55
  • ISSN: 0011-4642

Abstract

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The local well-posedness for the Cauchy problem of the liquid crystals system in the critical Besov space B ˙ p , 1 n / p - 1 ( n ) × B ˙ p , 1 n / p ( n ) with n < p < 2 n is established by using the heat semigroup theory and the Littlewood-Paley theory. The global well-posedness for the system is obtained with small initial datum by using the fixed point theorem. The blow-up results for strong solutions to the system are also analysed.

How to cite

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Ming, Sen, et al. "The Cauchy problem for the liquid crystals system in the critical Besov space with negative index." Czechoslovak Mathematical Journal 67.1 (2017): 37-55. <http://eudml.org/doc/287923>.

@article{Ming2017,
abstract = {The local well-posedness for the Cauchy problem of the liquid crystals system in the critical Besov space $\dot\{B\}_\{p,1\}^\{n/p-1\}(\mathbb \{R\}^n)\times \dot\{B\}_\{p,1\}^\{n/p\}(\mathbb \{R\}^n)$ with $n<p<2n$ is established by using the heat semigroup theory and the Littlewood-Paley theory. The global well-posedness for the system is obtained with small initial datum by using the fixed point theorem. The blow-up results for strong solutions to the system are also analysed.},
author = {Ming, Sen, Yang, Han, Chen, Zili, Yong, Ls},
journal = {Czechoslovak Mathematical Journal},
keywords = {liquid crystals system; critical Besov space; negative index; well-posedness; blow-up},
language = {eng},
number = {1},
pages = {37-55},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The Cauchy problem for the liquid crystals system in the critical Besov space with negative index},
url = {http://eudml.org/doc/287923},
volume = {67},
year = {2017},
}

TY - JOUR
AU - Ming, Sen
AU - Yang, Han
AU - Chen, Zili
AU - Yong, Ls
TI - The Cauchy problem for the liquid crystals system in the critical Besov space with negative index
JO - Czechoslovak Mathematical Journal
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 1
SP - 37
EP - 55
AB - The local well-posedness for the Cauchy problem of the liquid crystals system in the critical Besov space $\dot{B}_{p,1}^{n/p-1}(\mathbb {R}^n)\times \dot{B}_{p,1}^{n/p}(\mathbb {R}^n)$ with $n<p<2n$ is established by using the heat semigroup theory and the Littlewood-Paley theory. The global well-posedness for the system is obtained with small initial datum by using the fixed point theorem. The blow-up results for strong solutions to the system are also analysed.
LA - eng
KW - liquid crystals system; critical Besov space; negative index; well-posedness; blow-up
UR - http://eudml.org/doc/287923
ER -

References

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