LARGE TIME ASYMPTOTIC BEHAVIOR OF THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN PARTIAL SPACE-PERIODIC DOMAINS

doi:10.1016/S0252-9602(16)30061-3

Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (4): 1167-1191.doi: 10.1016/S0252-9602(16)30061-3

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LARGE TIME ASYMPTOTIC BEHAVIOR OF THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN PARTIAL SPACE-PERIODIC DOMAINS

Zhengzi CAO¹, Huicheng YIN², Lin ZHANG¹, Lu ZHU³

1 Department of Mathematics and IMS, Nanjing University, Nanjing 210093, China;
2 School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China;
3 College of Science, Hohai University, Nanjing 210098, China

Received:2015-07-29 Revised:2016-01-25 Online:2016-08-25 Published:2016-08-25
Contact: Huicheng YIN,E-mail:huicheng@nju.edu.cn E-mail:huicheng@nju.edu.cn
Supported by:
This project was supported by the NSFC (11571177) and the Priority Academic Program Development of Jiangsu Higher Education Institutions; Zhu Lu was also supported by the Fundamental Research Funds for the Central Universities (2014B14014).

Abstract

Abstract:

In this article, we study the large time behavior of the 3-D isentropic compressible Navier-Stokes equation in the partial space-periodic domains, and simultaneously show that the related profile systems can be described by like Navier-Stokes equations with suitable "pressure" functions in lower dimensions. Our proofs are based on the energy methods together with some delicate analysis on the corresponding linearized problems.

Key words: Large time behavior, profile system, energy method, partial space-periodic domain, Fourier series

CLC Number:

35Q30

Zhengzi CAO, Huicheng YIN, Lin ZHANG, Lu ZHU. LARGE TIME ASYMPTOTIC BEHAVIOR OF THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN PARTIAL SPACE-PERIODIC DOMAINS[J].Acta mathematica scientia,Series B, 2016, 36(4): 1167-1191.

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References

[1] Adams R A. Sobolev spaces. Pure and Applied Mathematics, Vol. 65. New York-London:Academic Press, 1975
[2] Duan Renjun, Ma Hongfang. Global existence and convergence rates for the 3-D compressible Navier-Stokes equations without heat conductivity. Indiana Univ Math J, 2008, 57(5):2299-2319
[3] Duan Renjun, Liu Hongxia, Ukai S, Yang Tong. Optimal L^p-L^q convergence rates for the compressible Navier-Stokes equations with potential force. J Differential Equations, 2007, 238(1):220-233
[4] Hoff D, Zumbrun K. Multi-dimensional diffusion waves for the Navier-Stokes equations of compressible flow. Indiana Univ Math J, 1995, 44(2):603-676
[5] Hoff D, Zumbrun K. Poinwise decay estimates for multidimensional Navier-Stokes diffusion waves. Z Angew Math Phys, 1997, 48(4):597-614
[6] Ishihara Y, Kagei Y. Large time behavior of the semigroup on L^p spaces associated with the linearized compressible Navier-Stokes equation in a cylindrical domain. J Differential Equations, 2010, 248:252-286
[7] Kagei Y. Large time behavior of solutions to the compressible Navier-Stokes equation in an infinite layer. Hiroshima Math J, 2008, 38(1):95-124
[8] Kagei Y. Asymptotic behavior of solutions to the compressible Navier-Stokes equation around a parallel flow. Arch Ration Mech Anal, 2012, 205(2):585-650
[9] Kagei Y, Nukumizu T. Asymptotic behavior of solutions to the compressible Navier-Stokes equation in a cylindrical domain. Osaka J Math, 2008, 4:987-1026
[10] Kobayashi T. Some estimates of solutions for the equations of motion of compressible viscous fluid in the three-dimensional exterior domain. J Differential Equations, 2002, 184:587-619
[11] Li Hailiang, Zhang Ting. Large time behavior of isentropic Compressible Navier-Stokes system in R³. Math Methods Appl Sci, 2011, 34(6):670-682
[12] Liu Tai-Ping, Wang Weike. The pointwise estimates of diffusion wave for the Navier-Stokes systems in odd multi-dimensions. Comm Math Phys, 1998, 196(1):145-173
[13] Matsumura A, Nishida T. The initial value problem for the equation of motion of viscous and heatconductive gases. J Math Kyoto Univ, 1980, 20(1):67-104
[14] Matsumura A, Nishida T. Initial boudary value problems for the equations of motion of general fluids. Comput Methods Appl Sci Eng V, 1982:389-406
[15] Matsumura A, Nishida T. Initial boudary value problems for the equations of motion of compressible viscous and heat conductive fluids. Commun Math Phys, 1983, 89:445-464
[16] Tani A. On the first initial-boundary value problem of compressible viscous fluid motion. Publ RIMS Kyoto Univ, 1977, 13:193-253

LARGE TIME ASYMPTOTIC BEHAVIOR OF THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN PARTIAL SPACE-PERIODIC DOMAINS

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