Guangwu WANG , Boling GUO . EXISTENCE AND UNIQUENESS OF THE WEAK SOLUTION TO THE INCOMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ MODELIN 2-DIMENSION[J]. Acta mathematica scientia, Series B, 2017 , 37(5) : 1361 -1372 . DOI: 10.1016/S0252-9602(17)30078-4

[1] Fan J S, Gao H J, Guo B L. Regularity critera for the Navier-Stokes-Landau-Lifshitz system. J Math Anal Appl, 2010, 363:29-37
[2] Guo B L, Ding S J. Landau-Lifshitz Equations. Singapore:Word Science, 2008
[3] Zhou Y L, Sun H S, Guo B L. Existence of weak solution for boundary problems of systems of ferromagnetic chain. Science in China A, 1981, 27:779-811
[4] Alouges F, Soyeur A. On global weak solutions for Landau-Lifshitz equations:Existence and nonuniqueness. Nonlinear Anal TMA, 1992, 18:1071-1084
[5] Zhou Y L, Guo B L, Tan S B. Existence and unqiness of smooth solution for system of ferromagnetic chain. Science in China, Ser A, 1991, 34:257-266
[6] Guo B L, Hong M C. The Landau-Lifshitz equations of the ferromagnetic spin chain and harmonic maps. Calc Var, 1993, 1:311-334
[7] Chen Y, Ding S J, Guo B L. Partial regularity for two-dimensional Landau-Lifshitz equations. Acta Math Sinica, New Ser, 1998, 14:423-432
[8] Chen Y, Struwe M. Existence and partial regularity results for the heat flow of harmonic maps. Math Z, 1989, 201:83-103
[9] Ding S J, Guo B L. Existence of partial regularity weak solutions to Landau-Lifshitz-Maxwell equations. J Differ Equ, 2008, 244(10):2448-2472
[10] Ding S J, Guo B L, Lin J Y, Zeng M. Global existence of weak solution for Landau-Lifshitz-Maxwell equtions. Discr Contin Dyn Syst, Series A, 2007, 17(4):867-890
[11] Guo B L, Su F Q. Global weak solution for the Landau-Lifshitz-Maxwell equations in three space dimensions. J Math Anal Appl, 1997, 211:326-346
[12] Guo B L, Su F Q. The global smooth solution for Landau-Lifshitz-Maxwell equations without dissipation. J Partial Diff Eqns, 1998, 11(3):193-208
[13] Guo B L, Su F Q. The attractors for Landau-Lifshitz-Maxwell equations. J Partial Diff Eqns, 2001, 14(2):133-148
[14] Guo B L, Wang B. Global existence of the solution for the Landau-Lifshitz equation of the ferromagnetic spin chain. Math Sin, 1997, 17:429-436
[15] Harpes P. Partial compactness for the 2-D Landau-Lifshitz flow. Elect J Diff Eqns, 2004, 90:1-24
[16] Kou Y L, Ding S J. Partial compactress for Landau-Lifshitz-Maxwell equation in two-dimension. Acta Math Sci, 2011, 31B(2):727-748
[17] Liu X. Partial regularity for Landau-Lifshitz system of ferromagnetic spin chain. Calc Var, 2004, 20:153-173
[18] Fefferman C, Stein E. H^p space of several variables. Acta Math, 1972, 129:137-193
[19] Moser R. Partial regularity for the Landau-Lifshitz equation in small dimension. Preprint 26, Max-PlanokInstitute for Mathematics in Science, 2002
[20] Melcher C. Existence of partially regular solutions for Landau-Lifshitz equations in R³. Comm Partial Differ Equ, 2005, 30:567-587
[21] Wang C Y. On Landau-Lifshitz equation in dimensions at most four. Indiana Univ Math J, 2006, 55(5):1615-1644
[22] Wang C Y. On moving Ginzburg-Landau vortices. Comm Anal Geom, 2004, 12:1185-1199
[23] Lions P L. Mathematical Topic in Fluid Mechanics. Vol. 2, Compressible Models//Oxford Lectures Series in Mathematics and its Applications, Vol. 10, Oxford Science Publications. New York:The Clarendon Press, Oxford University Press, 1998
[24] Feireisl E. Dynamics of Viscous Compressible Fluids. Oxford:Oxford University Press, 2004
[25] Feireisl E, Novotný A., Petzeltová H. On the existence of globally defined weak solutions to the NavierStokes equations. J Math Fluid Mech, 2001, 3:358-392
[26] Jiang S, Zhang P. Global sphereically symmetric solutions of the compressible isentropic Navier-Stokes equations. Comm Math Phys, 2001, 215:559-581
[27] Luo T, Xin Z P, Yang T. Interface behavior of compressible Navier-Stokes equtions with vacuum. SIAM J Math Anal, 2000, 31:1175-1191
[28] Lions J L. Quelques Methodes de iésolution des Problèm aux Limites non Linéaires. Paris:Dunod, 1969
[29] Ladyzhenskaya O A. The Mathematical Theory of Viscous Incompressible Flow. English Translation, 2nd Ed. New York:Gordon and Breach, 1969
[30] Temam R. Navier-Stokes Equations, Studies in Mathematics and its Applications. Revised ed. New York:North-Holland Publishing Company, Amsterdam Oxford, 1979
[31] Lei Z, Li D, Zhang X Y. Remarks of global wellposedness of liquid crystal flows and heat flow of harmonic maps in two dimensions. Proc Amer Math Soc, 2012, 142(11):3801-3810