American Institute of Mathematical Sciences

Advanced
October  2015, 20(8): 2761-2763. doi: 10.3934/dcdsb.2015.20.2761

A note on 'Spin-polarized transport: Existence of weak solutions'

Carlos J. García-Cervera 1, and  Xiao-Ping Wang 2,

1. 

Mathematics Department, University of California, Santa Barbara, CA 93105, United States
2. 

Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

Received  October 2014 Revised  February 2015 Published  August 2015

The authors presented a proof of existence of weak solutions to a model for spin-polarized transport in ferromagnetic multilayers in [1]. The proof of the previous result is valid only in the case when the external current in parallel to the boundary of the domain. We present here an extension of that result, which applies to more general currents.
Keywords: ferromagnetism, Landau-Lifshitz equation, spin transport., Micromagnetics, spintronics.
Mathematics Subject Classification: Primary: 35R05, 58J35; Secondary: 35Q6.
Citation: Carlos J. García-Cervera, Xiao-Ping Wang. A note on 'Spin-polarized transport: Existence of weak solutions'. Discrete & Continuous Dynamical Systems - B, 2015, 20 (8) : 2761-2763. doi: 10.3934/dcdsb.2015.20.2761
References:
[1]

C. J. García-Cervera and X. P. Wang, Spin-Polarized transport: Existence of weak solutions,, Disc. Cont. Dyn. Sys., 7 (2007), 87.  doi: 10.3934/dcdsb.2007.7.87.  Google Scholar

show all references

References:
[1]

C. J. García-Cervera and X. P. Wang, Spin-Polarized transport: Existence of weak solutions,, Disc. Cont. Dyn. Sys., 7 (2007), 87.  doi: 10.3934/dcdsb.2007.7.87.  Google Scholar

[1]

Xueke Pu, Boling Guo, Jingjun Zhang. Global weak solutions to the 1-D fractional Landau-Lifshitz equation. Discrete & Continuous Dynamical Systems - B, 2010, 14 (1) : 199-207. doi: 10.3934/dcdsb.2010.14.199
[2]

Tetsuya Ishiwata, Kota Kumazaki. Structure preserving finite difference scheme for the Landau-Lifshitz equation with applied magnetic field. Conference Publications, 2015, 2015 (special) : 644-651. doi: 10.3934/proc.2015.0644
[3]

Wei Deng, Baisheng Yan. On Landau-Lifshitz equations of no-exchange energy models in ferromagnetics. Evolution Equations & Control Theory, 2013, 2 (4) : 599-620. doi: 10.3934/eect.2013.2.599
[4]

Boling Guo, Fangfang Li. Global smooth solution for the Sipn-Polarized transport equation with Landau-Lifshitz-Bloch equation. Discrete & Continuous Dynamical Systems - B, 2020, 25 (7) : 2825-2840. doi: 10.3934/dcdsb.2020034
[5]

Ze Li, Lifeng Zhao. Convergence to harmonic maps for the Landau-Lifshitz flows between two dimensional hyperbolic spaces. Discrete & Continuous Dynamical Systems - A, 2019, 39 (1) : 607-638. doi: 10.3934/dcds.2019025
[6]

Jian Zhai, Zhihui Cai. $\Gamma$-convergence with Dirichlet boundary condition and Landau-Lifshitz functional for thin film. Discrete & Continuous Dynamical Systems - B, 2009, 11 (4) : 1071-1085. doi: 10.3934/dcdsb.2009.11.1071
[7]

Catherine Choquet, Mohammed Moumni, Mouhcine Tilioua. Homogenization of the Landau-Lifshitz-Gilbert equation in a contrasted composite medium. Discrete & Continuous Dynamical Systems - S, 2018, 11 (1) : 35-57. doi: 10.3934/dcdss.2018003
[8]

Stefan Possanner, Claudia Negulescu. Diffusion limit of a generalized matrix Boltzmann equation for spin-polarized transport. Kinetic & Related Models, 2011, 4 (4) : 1159-1191. doi: 10.3934/krm.2011.4.1159
[9]

Zonglin Jia, Youde Wang. Global weak solutions to Landau-Lifshtiz systems with spin-polarized transport. Discrete & Continuous Dynamical Systems - A, 2020, 40 (3) : 1903-1935. doi: 10.3934/dcds.2020099
[10]

Jing Li, Boling Guo, Lan Zeng, Yitong Pei. Global weak solution and smooth solution of the periodic initial value problem for the generalized Landau-Lifshitz-Bloch equation in high dimensions. Discrete & Continuous Dynamical Systems - B, 2020, 25 (4) : 1345-1360. doi: 10.3934/dcdsb.2019230
[11]

Carlos J. Garcia-Cervera, Xiao-Ping Wang. Spin-polarized transport: Existence of weak solutions. Discrete & Continuous Dynamical Systems - B, 2007, 7 (1) : 87-100. doi: 10.3934/dcdsb.2007.7.87
[12]

Shijin Ding, Boling Guo, Junyu Lin, Ming Zeng. Global existence of weak solutions for Landau-Lifshitz-Maxwell equations. Discrete & Continuous Dynamical Systems - A, 2007, 17 (4) : 867-890. doi: 10.3934/dcds.2007.17.867
[13]

Leif Arkeryd. A kinetic equation for spin polarized Fermi systems. Kinetic & Related Models, 2014, 7 (1) : 1-8. doi: 10.3934/krm.2014.7.1
[14]

Guangwu Wang, Boling Guo. Global weak solution to the quantum Navier-Stokes-Landau-Lifshitz equations with density-dependent viscosity. Discrete & Continuous Dynamical Systems - B, 2019, 24 (11) : 6141-6166. doi: 10.3934/dcdsb.2019133
[15]

Evelyne Miot, Mario Pulvirenti, Chiara Saffirio. On the Kac model for the Landau equation. Kinetic & Related Models, 2011, 4 (1) : 333-344. doi: 10.3934/krm.2011.4.333
[16]

D. Blömker, S. Maier-Paape, G. Schneider. The stochastic Landau equation as an amplitude equation. Discrete & Continuous Dynamical Systems - B, 2001, 1 (4) : 527-541. doi: 10.3934/dcdsb.2001.1.527
[17]

Gilles Carbou, Pierre Fabrie, Olivier Guès. On the Ferromagnetism equations in the non static case. Communications on Pure & Applied Analysis, 2004, 3 (3) : 367-393. doi: 10.3934/cpaa.2004.3.367
[18]

Proscovia Namayanja. Chaotic dynamics in a transport equation on a network. Discrete & Continuous Dynamical Systems - B, 2018, 23 (8) : 3415-3426. doi: 10.3934/dcdsb.2018283
[19]

Ioana Ciotir, Nicolas Forcadel, Wilfredo Salazar. Homogenization of a stochastic viscous transport equation. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020070
[20]

Kay Kirkpatrick. Rigorous derivation of the Landau equation in the weak coupling limit. Communications on Pure & Applied Analysis, 2009, 8 (6) : 1895-1916. doi: 10.3934/cpaa.2009.8.1895

2019 Impact Factor: 1.27

Tools

Metrics

  • PDF downloads (36)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences