三维广义磁流体方程组解的最优衰减率

南志杰, 吴刚

数学学报 ›› 2018, Vol. 61 ›› Issue (1) : 1-18.

PDF(642 KB)
PDF(642 KB)
数学学报 ›› 2018, Vol. 61 ›› Issue (1) : 1-18. DOI: 10.12386/A2018sxxb0001
论文

三维广义磁流体方程组解的最优衰减率

    南志杰1,2, 吴刚3
作者信息 +

Optimal Decay Estimates of Solutions to the Three-dimensional Generalized MHD Equations

    Zhi Jie NAN1,2, Gang WU3
Author information +
文章历史 +

摘要

本文利用Fourier分解法首次建立了三维广义磁流体动力学方程组弱解的时间衰减估计,得到了该方程解关于时间衰减的上下界估计,并且获得了相应的最优代数衰减率.

Abstract

We use Fourier-splitting method to establish the temporal decay estimates for weak solutions to the 3D generalized magneto-hydrodynamics equations firstly. We obtain not only the upper bounds estimates but also the lower bounds estimates of time decay for the solutions of these equations, moreover, the corresponding optimal algebraic time decay rates are found.

关键词

广义磁流体方程组 / Fourier分解法 / 最优衰减率

Key words

GMHD equations / Fourier-splitting method / optimal decay rates

引用本文

导出引用
南志杰, 吴刚. 三维广义磁流体方程组解的最优衰减率. 数学学报, 2018, 61(1): 1-18 https://doi.org/10.12386/A2018sxxb0001
Zhi Jie NAN, Gang WU. Optimal Decay Estimates of Solutions to the Three-dimensional Generalized MHD Equations. Acta Mathematica Sinica, Chinese Series, 2018, 61(1): 1-18 https://doi.org/10.12386/A2018sxxb0001

参考文献

[1] Jiu Q., Yu H., Decay of solutions to the three-dimensional generalized Navier-Stokes equations, Asymptotic Analysis, 2015, 94:105-124.
[2] Kato T., Strong Lp-solutions of the Navier-Stokes equations in Rm, with applications to weak solutions, Math. Z., 1984, 187:471-480.
[3] Leray J., Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Math., 1934, 63:193-248.
[4] Majda J., Bertozzi L., Vorticity and Incompressible Flow, Cambribge Texts in Applied Mathematics No. 27, 2002.
[5] Schonbek M., Decay of parabolic conservation laws, Comm. Part. Diff. Equ., 1980, 7:449-473.
[6] Schonbek M., L2 decay for weak solutions of the Navier-Stokes, Arch. Rat. Mech. Anal., 1985, 88:209-222.
[7] Schonbek M., Large time behavior of solutions to the Navier-Stokes equations, Comm. Part. Diff. Equ., 1985, 11:733-763.
[8] Schonbek M., Lower bounds of rates of decay for solutions to the Navier-Stokes equations, J. mer. Math., 1991, 4:423-449.
[9] Schonbek M., Schonbek T., Suli E., Large time behavior of solutions to the magneto-hydrodynamics equations, Math. Ann., 1996, 304:717-756.
[10] Stein E., Singular Integrals and Differentiability Properties of Functions, Princeton University, Princeton, USA, 1970.
[11] Temam R., Navier-Stokes Equations, North-Holland Publishing Company, Amsterdam, 1979.
[12] Wu J., Generalized MHD equations, J. Diff. Equ., 2003, 195:284-312.
[13] Zhou Y., Regularity criteria for the generalized viscous MHD equations, Ann. Inst. Henri. Poincaré, 2007, 24:491-505.

基金

国家自然科学基金资助项目(11101405);浙江省教育厅科研项目(Y201330036)

PDF(642 KB)

Accesses

Citation

Detail

段落导航
相关文章

/