LARGE TIME BEHAVIORS OF THE ISENTROPIC BIPOLAR COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM

doi:10.1016/S0252-9602(11)60357-3

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (5): 1725-1740.doi: 10.1016/S0252-9602(11)60357-3

LARGE TIME BEHAVIORS OF THE ISENTROPIC BIPOLAR COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM

邹晨

Department of Mechanics and Aerospace Engineering, Peking University, Beijing 100871, China

收稿日期:2010-07-05 出版日期:2011-09-20 发布日期:2011-09-20
基金资助:
This research is partially supported by NSFC (10872004), National Basic Research Program of China (2010CB731500), and the China Ministry of Education (200800010013).

LARGE TIME BEHAVIORS OF THE ISENTROPIC BIPOLAR COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM

ZOU Chen

Department of Mechanics and Aerospace Engineering, Peking University, Beijing 100871, China

Received:2010-07-05 Online:2011-09-20 Published:2011-09-20
Supported by:
This research is partially supported by NSFC (10872004), National Basic Research Program of China (2010CB731500), and the China Ministry of Education (200800010013).

摘要/Abstract

摘要：

The isentropic bipolar compressible Navier-Stokes-Poisson (BNSP) system is investigated in R3 in the present paper. The optimal time decay rate of global strong solution is established. When the regular initial data belong to the Sobolev space H^l(R³)∩˙B^−s_1,1(R³) with l ≥ 4 and s ∈ (0, 1], it is shown that the momenta of the charged particles decay at the optimal rate (1+t)^−1/4−s/2 in L²-norm, which is slower than the rate (1+t)^−3/4−s/2 for the compressible Navier-Stokes (NS) equations [14]. In particular, a new phenomenon on the charge transport is observed. The time decay rate of total density and momentum was both (1 + t)^−3/4 due to the cancellation effect from the interplay interaction of the charged particles.

关键词: bipolar Navier-Stokes-Poisson system, optimal time convergence rate, total momentum

Abstract:

Key words: bipolar Navier-Stokes-Poisson system, optimal time convergence rate, total momentum

中图分类号:

35B40

邹晨. LARGE TIME BEHAVIORS OF THE ISENTROPIC BIPOLAR COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM[J]. 数学物理学报(英文版), 2011, 31(5): 1725-1740.

ZOU Chen. LARGE TIME BEHAVIORS OF THE ISENTROPIC BIPOLAR COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM[J]. Acta mathematica scientia,Series B, 2011, 31(5): 1725-1740.

参考文献

[1] Degond P, Jin S, Liu J. Mach-number uniform asymptotic-preserving gauge schemes for compressible flows. Bull Inst Math Acad Sin (N S), 2007, 2(4): 851–892

[2] Donatelli D. Local and global existence for the coupled Navier-Stokes-Poisson problem. Quart Appl Math, 2003, 61: 345–361

[3] Donatelli D, Marcati P. A quasineutral type limit for the Navier-Stokes-Poisson system with large data. Nonlinearity, 2008, 21(1): 135–148

[4] Duan R-J, Liu H, Ukai S, Yang T. Optimal L^p − L^qconvergence rates for the compressible Navier-Stokes equations with potential force. J Diff Eqns, 2007, 238(5): 220–233

[5] Ducomet B, Feireisl E, Petzeltova H, Skraba I S. Global in time weak solution for compressible barotropic self-gravitating fluids. Discrete Continues Dynamical System, 2004, 11(1): 113–130

[6] Ducomet B, Zlotnik A. Stabilization and stability for the spherically symmetric Navier-Stokes-Poisson system. Appl Math Lett, 2005, 18(10): 1190–1198

[7] Hao C, Li H-L. Global Existence for compressible Navier-Stokes-Poisson equations in three and higher dimensions. J Diff Eqns, 2009, 246: 4791–4812

[8] Hoff D, Zumbrun K. Multi-dimensional diffusion waves for the Navier-Stokes equations of compressible flow. Indiana Univ Math J, 1995, 44: 603–676

[9] Hoff D, Zumbrun K, Pointwise decay estimates for multidimensional Navier-Stokes diffusion waves. Z Angew Math Phys, 1997, 48: 597–614

[10] Ju Q, Li F, Li H-L. The quasineutral limit of Navier-Stokes-Poisson system with heat conductivity and general initial data. J Diff Eqns, 2009, 247: 203–224

[11] Kobayashi T, Suzuki T. Weak solutions to the Navier-Stokes-Poisson equations. 2004, preprint

[12] Li H-L, Matsumura A, Zhang G. 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: 1721–1736

[14] Li H-L, Zhang T. Large time behavior of isentropic compressible Navier-Stokes system in R3. preprint

[15] Liu T-P, Wang W-K. The pointwise estimates of diffusion waves for the Navier-Stokes equations in odd multi-dimensions. Comm Math Phys, 1998, 196: 145–173

[16] Markowich P A, Ringhofer C A, Schmeiser C. Semiconductor Equations. New York: Springer-Verlag, 1990

[17] Matsumura A, Nishida T. The initial value problem for the equations of motion of compressible viscous and heat-conductive fluids. Proc Japan Acad, 1979, 55(A), 337–342

[18] Matsumura A, Nishida T. The initial value problem for the equations of motion of viscous and heat-conductive gases. J Math Kyoto Univ, 1980, 20: 67–104

[19] Ponce G. Global existence of small solution to a class of nonlinear evolution equations. Nonlinear Anal, 1985, 9: 339–418

[20] Wang S, Jiang S. The convergence of the Navier-Stokes-Poisson system to the incompressible Euler equa-tions. Comm Partial Diff Eqns, 2006, 31: 571–591

[21] Zhang G, Li H-L, Zhu C. Optimal decay rate of the non-isentropic compressible Navier-Stokes-Poisson system in R3. J Diff Eqns, 2010, 25(2): 866–891

[22] Zhang Y, Tan Z. On the existence of solutions to the Navier-Stokes-Poisoon equations of a two-dimensional compressible flow. Math Methods Appl Sci, 2007, 30(3): 305–329

LARGE TIME BEHAVIORS OF THE ISENTROPIC BIPOLAR COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM

LARGE TIME BEHAVIORS OF THE ISENTROPIC BIPOLAR COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM

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