Acta mathematica scientia, Series B >
POINTWISE ESTIMATES OF SOLUTION FOR NON-ISENTROPIC NAVIER-STOKES-POISSON EQUATIONS IN MULTI-DIMENSIONS
Received date: 2011-06-29
Online published: 2012-09-20
Supported by
The research of Z.G. Wu was supported by National Natural Science Foundation of China (11101112), and the research of W.K. Wang was supported by National Natural Science Foundation of China (11071162).
The Cauchy problem of the non-isentropic Navier-Stokes-Poisson equations in multi-dimensions is considered. The global existence and pointwise estimates of the classical solution are given, which extend the optimal decay rate in L2-norm in [27] to the Lp(Rn) (p > n/n−1 )-norm.
Key words： hyperbolic-parabolic-elliptic system; Greens function
WU Zhi-Gang , WANG Wei-Ke . POINTWISE ESTIMATES OF SOLUTION FOR NON-ISENTROPIC NAVIER-STOKES-POISSON EQUATIONS IN MULTI-DIMENSIONS[J]. Acta mathematica scientia, Series B, 2012 , 32(5) : 1681 -1702 . DOI: 10.1016/S0252-9602(12)60134-9
[1] Degond P. Some Current Topics on Nonlinear Conservation Laws. AMS/IP Studies in Advanced Mathe-matics Vol 15. Providence, RI: Amer Math Soc, 2000: 77–110
[2] Donatelli D. Local and global existence for the coupled Navier-Stokes-Poisson problem. Quart Appl Math, 2003, 61(2): 345–361
[3] Duan R J, Ukai S, Yang T, Zhao H J. Optimal convergence rates for the compressible Navier-Stokes equations with potential forces. Math Models Methods Appl Sci, 2007, 17(5): 737–758
[4] Duan R J, Liu H X, Ukai S, Yang T. Optimal Lp −Lq convergence rates for the compressible Navier-Stokes equations with potential force. J Diff Eqns, 2007, 238(1): 220–233
[5] Ducomet B, Feireisl E, Petzeltova H, Skraba I S. Global in time weak solution for compressible barotropic self-gravitating fluids. Disc Contin Dyn Sys, 2004, 11(1): 113–130
[6] Ducomet B. A remark about global existence for the Navier-Stokes-Poisson system. Appl Math Lett, 1999, 12: 31–37
[7] Hoff D, Zumbrun K. Multi-dimensional diffusion wave for the Navier-Stokes equations of compressible flow. Indiana Univ Math J, 1995, 44(2): 603–676
[8] Hoff D, Zumbrun K. Pointwise decay estimates for multidimensional Navier-Stokes diffusion waves. Z Angew Math Phys, 1997, 48: 1–18
[9] Hsiao L, Markowich P A, Wang S. The asymptotic behavior of globally smooth solutions fo the multidi-mensional isentropic hydrodynamic model for semiconductors. J Diff Eqns, 2003, 192: 111–133
[10] Hsiao L, Li H L. Compressible navier-stokes-poisson equations. Acta Math Sci, 2010, 30B(6): 1937–1948
[11] Kawashima S. System of a hyperbolic-parabolic composite type, with applications to the equations of Manetohydrodynamics[D]. Kyoto: Kyoto University, 1983
[12] Li H L, Matsumura A, Zhang G J. Optimal decay rate of the compressible Navier-Stokes-Poisson system in R3. Arch Ration Mech Anal, 2010, 196: 681–713
[13] Li H L, Yang T, Zou C. Time asymptotic behavior of the bipolar Navier-Stokes-Poisson system. Acta Math Sci, 2009, 29B(6): 1721–1736
[14] Li D L. The Green’s function of the Navier-Stokes equations for gas dynamics in R3. Comm Math Phys, 2005, 257: 579–619
[15] Liu T P, Wang W K. The pointwise estimates of diffusion wave for the Navier-Stokes systems in odd multi-dimension. Commum Math Phys, 1998, 196: 145–173
[16] Liu T P, Zheng Y N. Large time behavior of solutions general quasilinear hyperbolic-parabolic systems of conservation laws. Mem Amer Math Soc, 1997, 599
[17] Matsumura A, Nishida T. The initial value problem for the equation of motion of compressible viscous and heat-conductive fluids. Proc Japan Acad Ser A, 1979, 55: 337–342
[18] Matsumura A, Nishida T. The initial value problem for the equation of motion of viscous and heat-conductive gases. J Math Kyoto Univ, 1980, 20: 67–104
[19] Matsumura A, Nishida T. Initial boundary value problems for the equations of motion of compressible viscous and heat conductive fluids. Comm Math Phys, 1983, 89(2): 445–464
[20] Solonnikov V A. Evolution free boundary problem for equations of motion of viscous compressible self-gravitating fluid. SAACM 1993, 3: 257–275
[21] Ukai S, Yang T, Zhao H J. Convergence rate for the compressible Navier-Stokes equations with external force. J Hyperbolic Diff Eqns, 2006, 3: 561–574
[22] Wang W K, Yang T. The pointwise estimates of solutions for Euler-Equations with damping in multi-dimensions. J Diff Eqns, 2001, 173: 410–450
[23] Wang W K, Yang X F. The pointwise estimates of solutions to the isentropic Navier-Stokes equations in even space-dimensions. J Hyperbolic Diff Eqns, 2005, 2(3): 673–695
[24] Wang W K, Wu Z G. Pointwise estimates of solution for the Navier-Stokes-Poisson equations in multi-dimensions. J Diff Eqns, 2010, 248: 1617–1636
[25] Wang W K. Nonlinear evolution systems and green’s function. Acta Math Sci, 2010, 30B(6): 2051–2063
[26] Wu Z G. Regularity and asymptotic behavior of 1D compressible Navier-Stokes-Poisson equations with free boundary. J Math Anal Appl, 2011, 374: 29–48
[27] Zhang Y H, Tan Z. On the existence of solutions to the Navier-Stokes-Poisson equations of a two-dimensional compressible flow. Math Meth Appl Sci, 2007, 30: 305–329
[28] Zhang G J, Li H L, Zhu C J. Optimal decay rate of the non-isentropic Navier-Stokes-Poisson system in R3. J Diff Eqns, 2011, 250(2): 866–891
[29] Zhang T, Fang D Y. Global behavior of spherically symmetric Navier-Stokes-Poisson system with degen-erate viscosity coefficients. Arch Rational Mech Anal, 2009, 191: 195–243
/
| 〈 |
|
〉 |