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二维不可压缩 Navier--Stokes--Landau--Lifshitz 方程组的整体强解

黄丙远

黄丙远. 二维不可压缩 Navier--Stokes--Landau--Lifshitz 方程组的整体强解[J]. 华南师范大学学报(自然科学版), 2017, 49(6): 113-118. doi: 10.6054/j.jscnun.2017167
引用本文: 黄丙远. 二维不可压缩 Navier--Stokes--Landau--Lifshitz 方程组的整体强解[J]. 华南师范大学学报(自然科学版), 2017, 49(6): 113-118. doi: 10.6054/j.jscnun.2017167
Huang Bingyuan. Global Smooth Solutions for the 2D incompressibleNavier--Stokes--Landau--Lifshitz equations[J]. Journal of South China normal University (Natural Science Edition), 2017, 49(6): 113-118. doi: 10.6054/j.jscnun.2017167
Citation: Huang Bingyuan. Global Smooth Solutions for the 2D incompressibleNavier--Stokes--Landau--Lifshitz equations[J]. Journal of South China normal University (Natural Science Edition), 2017, 49(6): 113-118. doi: 10.6054/j.jscnun.2017167

二维不可压缩 Navier--Stokes--Landau--Lifshitz 方程组的整体强解

doi: 10.6054/j.jscnun.2017167
基金项目: 

国家自然科学基金青年科学基金项目;国家自然科学基金数学天元基金项目;广东省教育厅青年创新人才类项目

详细信息
    通讯作者:

    黄丙远

  • 中图分类号: O175. 4

Global Smooth Solutions for the 2D incompressibleNavier--Stokes--Landau--Lifshitz equations

More Information
    Corresponding author: Huang Bingyuan
  • 摘要: 考虑了不可压缩 Navier--Stokes--Landau--Lifshitz 耦合模型在二维空间中的Cauchy 问题, 假设在初值密度满足$\rho_00$及初值能量具备$\|\rho_0^\frac{1}{2}\mathbf{u}_0\|_{L^2}^2+\|\nabla\mathbf{d}_0\|_{L^2}^2 \varepsilon_0$足够小的条件下, 利用能量方法证明了整体强解的存在唯一性.
  • [1]Fan J, Gao H, Guo B.Regularity criteria for the Navier--Stokes--Landau--Lifshitz system[J].Journal of Mathematical Analysis and Applications, 2010, 363(1):29-37 [2]Zhai X, Li Y, Yan W.Global solutions to the Navier--Stokes--Landau--Lifshitz system[J]., 2015, :- [3]Jun Choe H, Kim H.Strong solutions of the Navier--Stokes equations for nonhomogeneous incompressible fluids[J].Communications in Partial Differential Equations, 2003, 28(5):1183-1201 [4]Kim H.A Blow Up Criterion for the Nonhomogeneous Incompressible Navier--Stokes Equations[J].SIAM journal on mathematical analysis, 2006, 37(5):1417-1434 [5]GUO B L, DING S J.Landau-Lifschitz Equations[M]. Singapore, World Scientific, 2008. [6]Wen H Y, Ding S J.Solutions of incompressible hydrodynamic flow of liquid crystals[J].Nonlinear Analysis: Real World Applications, 2011, 12(3):1510-1531 [7]Lin F H, Lin J Y, Wang C Y.Liquid crystal flows in two dimensions[J].Arch. Ration. Mech. Anal, 2010, 197(1):297-336 [8]Ding S J, Huang J R, Xia F G.Global existence of strong solutions for incompressible hydrodynamic flow of liquid crystals with vacuum[J].Filomat, 2013, 27(7):1247-1257 [9]丁时进.液晶模型的分析理论[J].华南师范大学学报自然科学版, 2013, 45(3):1-7 [10]Huang T, Wang C Y, Wen H Y.Strong solutions of the compressible nematic liquid crystal flow[J].J. Diff. Eqs, 2012, 252(3):2222-2265 [11]Nirenberg L.On elliptic partial differential equations[J].Annali della Scuola Normale Superiore di Pisa--Classe di Scienze, 1959, 13(2):115-162 [12]Ladyzhenskaya O A, Solonnikov V A.Unique solvability of an initial and boundary value problem for viscous incompressible nonhomogeneous fluids[J].Journal of Soviet Mathematics, 1978, 9(5):697-749 [13]Galdi G P.An introduction to the mathematical theory of the Navier-Stokes equations. Linearized Steady Problems, Vol.1, Springer Tracts in Natural Philosophy. Vol.38[M], New York, Springer-Verlag, 1994.

    [1]Fan J, Gao H, Guo B.Regularity criteria for the Navier--Stokes--Landau--Lifshitz system[J].Journal of Mathematical Analysis and Applications, 2010, 363(1):29-37 [2]Zhai X, Li Y, Yan W.Global solutions to the Navier--Stokes--Landau--Lifshitz system[J]., 2015, :- [3]Jun Choe H, Kim H.Strong solutions of the Navier--Stokes equations for nonhomogeneous incompressible fluids[J].Communications in Partial Differential Equations, 2003, 28(5):1183-1201 [4]Kim H.A Blow Up Criterion for the Nonhomogeneous Incompressible Navier--Stokes Equations[J].SIAM journal on mathematical analysis, 2006, 37(5):1417-1434 [5]GUO B L, DING S J.Landau-Lifschitz Equations[M]. Singapore, World Scientific, 2008. [6]Wen H Y, Ding S J.Solutions of incompressible hydrodynamic flow of liquid crystals[J].Nonlinear Analysis: Real World Applications, 2011, 12(3):1510-1531 [7]Lin F H, Lin J Y, Wang C Y.Liquid crystal flows in two dimensions[J].Arch. Ration. Mech. Anal, 2010, 197(1):297-336 [8]Ding S J, Huang J R, Xia F G.Global existence of strong solutions for incompressible hydrodynamic flow of liquid crystals with vacuum[J].Filomat, 2013, 27(7):1247-1257 [9]丁时进.液晶模型的分析理论[J].华南师范大学学报自然科学版, 2013, 45(3):1-7 [10]Huang T, Wang C Y, Wen H Y.Strong solutions of the compressible nematic liquid crystal flow[J].J. Diff. Eqs, 2012, 252(3):2222-2265 [11]Nirenberg L.On elliptic partial differential equations[J].Annali della Scuola Normale Superiore di Pisa--Classe di Scienze, 1959, 13(2):115-162 [12]Ladyzhenskaya O A, Solonnikov V A.Unique solvability of an initial and boundary value problem for viscous incompressible nonhomogeneous fluids[J].Journal of Soviet Mathematics, 1978, 9(5):697-749 [13]Galdi G P.An introduction to the mathematical theory of the Navier-Stokes equations. Linearized Steady Problems, Vol.1, Springer Tracts in Natural Philosophy. Vol.38[M], New York, Springer-Verlag, 1994.
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出版历程
  • 收稿日期:  2016-01-28
  • 修回日期:  2016-04-20
  • 刊出日期:  2017-12-25

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