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PDF(448 KB)
PDF(448 KB)
PLn∩PLp空间中MHD方程组强解的存在唯一性及衰减性质
Existence, Uniqueness and Decay Properties for Strong Solutions of the MHD Equations in Space PLn∩PLp
MHD方程组 / 强解 / 存在唯一性 / 衰减性质 {{custom_keyword}} /
MHD equations / strong solutions / existence and uniqueness / decay properties {{custom_keyword}} /
[1] Kato T., Strong Lp-solutions of the Navier--Stokes equation in Rm, with applications to weak solutions, Math. Z., 1984, 187: 471--480.
[2] Duvaut G., Lions J. L., Inéquations en thermoélasticité et Magnéto-hydrodynamic, Arch. Ration Mech. Anal., 1972, 46: 241--279.
[3] Sermange M., Temam R., Some mathematical questions related to the MHD equations, Comm. Pure Appl. Math., 1983, 36: 635--664.
[4] Kozono H., Weak and classical solutions of the two-dimensional Magneto-hydrodynamic equations, Tohoku Math. J., 1989, 41: 471--488.
[5] Caflisch R. E., Klapper I., Steele G., Remarks on singularities, dimension and energy dissipation for ideal hydrodynamic and MHD, Comm. Math. Phys., 1997, 184: 443--455.
[6] Beale J. T., Kato T., Majda A., Remarks on breakdown of smooth solutions for the 3D Euler equations, Comm. Math. Phys., 1984, 94: 61--66.
[7] Wu J., Regularity results for weak solutions of the 3D MHD equations, Discrete Contin. Dyn. Syst., 2004, 10: 543--556.
[8] Zhou Y., Remarks on regularities for the 3D MHD equations, Discrete Contin. Dyn. Syst., 2005, 12: 881--886.
[9] Zhou Y., Regularity criteria for the 3D MHD equations in terms of the pressure, Nonlinear Mech., 2006, 41: 1174--1180.
[10] He C., Xin Z., On the regularity of weak solutions to the Magneto-hydrodynamic equations, J. Differential Equations, 2005, 213: 235--254.
[11] Giga Y., Solutions for semilinear parabolic equations in L^p and regularity of weak solutions of the Navier--Stokes system, J. Differential Equations, 1986, 61: 186--212.
[12] Schonbek M. E., Schonbek T. P., Süli E., Large-time behavior of solution to the Magneto-hydrodynamic equations, Math. Ann., 304: 717--756.
[13] Chen Q. L., Miao C. X., Blow-up criterion of smooth solutions to the two-fluid MHD equations, arXiv: Math.AP/0611165v2, 10 Nov., 2006.
[14] Li D. Q., Chen Y. M., Nonlinear Evolution Equations, Beijing: Science Press, 1997 (in Chinese).
[15] Shang X. M., Existence, Uniqueness and Decay Properties for Solutions of the MHD Equations, Master Degree Dissertation, Beijing: Beijing Capital Normal University, 2005 (in Chinese).
国家自然科学基金(10301026,10225102)
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