[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.
(上接第720页)
[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. |