Abstract
We consider the existence of global attractor for non-Newtonian fluids near the BCS-BEC crossover in this paper. By Gronwall’s inequality, interpolar inequality and the techniques for proving regularity theory in partial differential equations, etc., we establish suitable prior estimates and obtain the global attractor for non-Newtonian fluids.
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Ball, J.M.: Continuity Properties and Global Attractors of Generalized Semiflows and the Navier-Stokes Equations. Mechanics: From Theory to Computation (1998)
Ball, J.M.: Global attractors for damped semilinear wave equations. Discrete Cont. Dynamical Sys. - Series A (DCDS-A) 10(1-2), 31–52 (2012)
Cheban, D., Mammana, C., Michetti, E.: Global Attractors of Non-autonomous Difference Equations. Working Papers 1(1), 45–57 (2008)
Chen, S., Guo, B.: On the Cauchy Problem of the Ginzburg-Landau Equations for atomic fermi gases near the BCS-BEC crossover. J. Partial Differ. Equ. 22(3), 218–233 (2009)
Chen, S., Guo, B.: classical solutions of time-dependent Ginzburg-Landau equations for atomic fermigases near the BCS-BEC crossover. J. Differ. Equ. 251(6), 1359–1368 (2011)
Chen, S., Guo, B.: Classical solutions of general Ginzburg - Landau equations. Acta Mathematica Scientia-English Series B 36B(3), 1–16 (2016)
Drechsler, M., Zwerger, W.: Crossover from BCS-supercoductivity to Bose-condensation. Ann.phy-s. 504(1), 15–23 (1992)
GongQing, Z., YuanQu, L.: Functional Analysis Handout, 1st edn. Peking University Press, BeiJing (2016)
Guo, B., Jiang, M.: Finite Dimensional Behavior of Global Attractors for Weakly Damping Ginzburg-Landau Equations Coupling with BBM Equations. Commun. Nonlinear Sci. Numer. Simul. 3(1), 10–14 (1998)
Lawrence, C.E.: Partial differential equations, 2nd edn. Higher Education Press, Beijing (2017)
LiYuan, Z.: On The theory of superconductivity. Peking University Press, BeiJing (2003)
MKoyama, M.: Time-dependent Ginzburg-Landau theory for atomic fermi gases near the BCS-BEC crossover. Phy.Rev. A 74, 033603 (2006)
Raugel, G.: Global Attractors in Partial Differential Equations. Handbook Dynamical Syst. Vol. 2 176(1), 885–982 (2000)
Sa de Melo, C.A.R., Randeria, M., Engelbrecht, J.R.: Crossover from BCS to bose superconductivity: transition temperature and time-dependent Ginzburg-Landau theory. Phys. Rev. Lett. 71, 3201–3205 (1993)
Sell, G.R.: Global attractors for the three-dimensional Navier-Stokes equations. J. Dynamics Differ. Equ. 8(1), 1–33 (1996)
Xingyou, Z., Xiaohong, H.: Global attractors of reaction-diffusion systems and their homogenization. Partial. Differ. Equ. (1) 80–88 (2004)
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Xiong, C., Chen, S. Global Attractors of Non-Newtonian Fluids Near the BCS-BEC Crossover. Math Phys Anal Geom 23, 24 (2020). https://doi.org/10.1007/s11040-020-09348-0
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DOI: https://doi.org/10.1007/s11040-020-09348-0