Research articles
ScienceAsia 51 (2023): 1-10 |doi:
10.2306/scienceasia1513-1874.2023.064
Global attractors for non-Newtonian equations on BCS-BEC
crossover
Chunyan Xionga, Shuhong Chenb,c,*
ABSTRACT: This paper considers the global attractor problem for the non-Newtonian equations on BCS (Bardeen
Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover. These non-Newtonian equations can be translated
into the time-dependent Ginzburg-Landau equations. In order to establish the attractors, we first prove the existence
and uniqueness theorem of weak solutions by the standard Faedo-Galerkin approximation method. Then, we establish
some suitable prior estimates of the weak solutions by combining Gagliardo-Nirenberg inequality, Agmon?s inequality
and Gronwall inequality, etc. Finally, using the existence theorem of the global attractor, we prove that there exists
a compact global attractor for the time dependent Ginzburg-Landau equations of BCS-BEC crossover on atomic fermi
gases near the Feshbach resonance.
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| a |
Institute of Electromagnetics and Acoustics School of Electronic Science and Engineering, Xiamen University,
Xiamen, Fujian 361005 China |
| b |
School of Information Engineering, Zhejiang Ocean University, Zhoushan, Zhejiang 316022 China |
| c |
School of Mathematics and Computer, Wuyi University, Wuyishan, Fujian 354300 China |
* Corresponding author, E-mail: shiny0320@163.com
Received 29 Mar 2023, Accepted 0 0000
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