［1］ Sermange M, Teman R. Some mathematical questions related to the MHD equations［J］. Comm Pure Appl Math, 1983, 36: 635-664.
［2］ Acheritogaray M, Degond P, Frouvelle A, et al. Kinetic formulation and global existence for the Hall-magneto-hydrodynamics system［J］. Kinet Relat Models, 2011, 4: 901-918.
［3］ Chae D, Degond P, Liu J. Well-posedness for Hall-magnetohydrodynamics［J］. Annales de lInstitut Henri Poincare (C) Non Linear Analysis, 2014, 31: 555-565.
［4］ Chae D, Schonbek M. On the temporal decay for the Hall-magnetohydrodynamic equations［J］. J Differential Equations, 2013, 255: 3 971-3 982.
［5］ Dong B, Li Y. Large time behavior to the system of incompressible non-Newtonian fluids in R2［J］. J Math Anal Appl, 2004, 298: 667-676.
［6］ Dong B, Chen Z. Asymptotic profiles of solutions to the 2D viscous incompressible micropolar fluid equations［J］. Discrete Contin Dyn Syst, 2009, 23: 765-784.
［7］ Dong B, Song J. Global regularity and asymptotic behavior of the modified Navier-Stokes equations with fractional dissipation［J］. Discrete and Continuous Dynamical Systems, 2012, 32: 57-79.
［8］ Guo Y, Wang Y. Decay of dissipative equations and negative Sobolev spaces［J］. Comm Partial Differential Equations, 2012, 37: 2 165-2 208.
［9］ Han P, He C. Decay properties of solutions to the incompressible magneto-hydrodynamics equations in a half space［J］. Math Methods Appl Sci, 2012, 35: 1 472-1 488.
［10］ He C, Xin Z. On the decay properties of solutions to the non-stationary Navier-Stokes equations in R3［J］. Proc Roy Soc Edinburgh Sect A, 2001, 131: 597-619.
［11］ Kajikiya R, Miyakawa T. On L2 decay of weak solutions of Navier-Stokes equations in Rn［J］. Math Zeit, 1986, 192: 135-148.
［12］ Oliver M, Titi E S. Remark on the rate of decay of higher order derivatives for solutions to the Navier-Stokes equations in Rn［J］. J Funct Anal, 2000, 172: 1-18.
［13］ Qin X, Wang Y. Large-time behavior of solutions to the inflow problem of full compressible Navier-Stokes equations［J］. SIAM J Math Anal, 2011, 43: 341-366.
［14］ Schonbek M E. L2 decay for weak solutions of the Navier-Stokes equations［J］. Arch Rational Mech Anal, 1985, 88: 209-222.
［15］ Schonbek M E, Schonbek T P, Süli E. Large-time behaviour of solutions to the magneto-hydrodynamics equations［J］. Math Ann, 1996, 304: 717-756.
［16］ Agapito R, Schonbek M E. Non-uniform decay of MHD equations with and without magnetic diffusion［J］. Comm Partial Differential Equations, 2007, 32: 1 791-1 812.
［17］ Wiegner M. Decay results for weak solutions of the Navier-Stokes equations in Rn［J］. J London Math Soc, 1987, 35: 303-313.
［18］ Zhang L. New results of general n-dimensional incompressible Navier-Stokes equations［J］. J Differential Equations, 2008, 245: 3 470-3 502.
［19］ Zhao C, Liang Y, Zhao M. Upper and lower bounds of time decay rate of solutions to a class of incompressible third grade fluid equations［J］. Nonlinear Anal Real World Appl, 2014, 15: 229-238.
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[4] Wu J, Ruan Q, Yang Y H. Gradient estimate for exponentially harmonic functions on complete Riemannian manifolds[J]. Manuscripta Mathematica, 2014, 143(3-4): 483-489.
[5] Kotschwar B, Ni L. Local gradient estimates of p-harmonic functions, 1/H-flow, and an entropy formula[J]. Annales scientifiques de lcole Normale Supérieure,2009, 42(1): 1-36.
[6] Li P, Yau S T. On the parabolic kernel of the Schrdinger operator[J]. Acta Mathematica, 1986, 156(1): 153-201.
[7] Wei G, Wylie W. Comparison geometry for the Bakry-Emery Ricci tensor[J]. Journal of Differential Geometry, 2009, 83(2): 337-405.
[8] Li P. Lecture notes on geometric analysis[R]. Seoul: Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, 1993. |
