HOMOGENIZATION OF THE INCOMPRESSIBLE NAVIER-STOKES FLUID WITH OSCILLATION COEFFICIENT

doi:10.1016/S0252-9602(13)60135-6

摘要/Abstract

摘要：

We study the homogenization of the incompressible Navier-Stokes equations with periodic oscillating coefficient in a bounded non-homogeneous media. To do that, we introduce a generalized compensate compactness result and a suitable class of test function to this problem. By passing the limit, we obtain the homogenized model of this problem.

关键词: Div-curl lemma, homogenization, Navier-Stokes equations

Abstract:

Key words: Div-curl lemma, homogenization, Navier-Stokes equations

中图分类号:

76D05

赵红星. HOMOGENIZATION OF THE INCOMPRESSIBLE NAVIER-STOKES FLUID WITH OSCILLATION COEFFICIENT[J]. 数学物理学报(英文版), 2014, 34(1): 183-193.

ZHAO Hong-Xing. HOMOGENIZATION OF THE INCOMPRESSIBLE NAVIER-STOKES FLUID WITH OSCILLATION COEFFICIENT[J]. Acta mathematica scientia,Series B, 2014, 34(1): 183-193.

参考文献

[1] Bensoussan, A, Lions J L, Papanicolaou G. Asymptotic Analysis for Periodic Structures. Studies of Mathematics and Its Application, Vol 5. North-Holland, 1978

[2] Sanchez-Palencia E. Nonhomogeneous Media and Vibration Theory. Lecture Notes in Physics, 127. Springer-Verlag, 1980

[3] Wall P. Some homogenization and corrector results for nonlinear monotone operators. J Nonlinear Math Phys, 1998, 5(3): 331–348

[4] Bystr¨om J. Correctors for some nonlinear monotone operators. J Nonlinear Math Phys, 2001, 8(1): 8–30

[5] Allaire G, Piatnitski A. Homogenization of the Schr¨odinger equation and effective mass theorems. Comm Math Phy, 2005, 258(1): 1–22

[6] Allaire G, Capdeboscq Y, Piatnitski A, Siess V, Vanninathan M. Homogenization of periodic systems with large potentials. Archive for Rational Mechanics and Analysis, 2004, 174(2): 179–220

[7] Allaire G. Dispersive limits in the homogenization of the wave equation. Annales de la Faculte des Sciences de Toulouse 2003, 12(4): 415–431

[8] Courilleau P, Mossino J. Compensated compactness for nonlinear homogenization and reduction of dimension.
Calculus of Variations and Partial Differential, 2004, 20(1): 65–91

[9] Courilleau P, Fabre S, Mossino J. Homogenization of some nonlinear problems with specific dependance upon coordinates. Boll Unione Mat Ital, 2001, 8B(4): 711–729

[10] Gustafssona B, Mossino J. Explicit limits for nonperiodic homogenization and reduction of dimension. Comptes Rendus Mathematique, 2002, 334(11): 977–982

[11] Tartar L. Compensated compactness and application to PDE//Nonlinear Analysis and Mechanics, Heriot-Watt Symposium IV. Research Notes in Math 39. Pitman, 1979: 136–212

[12] Tartar L. The compensated compactness method applied to systems of conversation laws//Systems of nonlinear PDE. Nato Asi series C III Reidel, 1983: 263–285

[13] Lions P L. Mathematical Topics in Fluid Mechanics, Vol 1. New York: The Clarendon Press, Oxford University Press, 1996

[14] Lions P L. Mathematical Topics in Fluid Mechanics, Vol 2. New York: The Clarendon Press, Oxford University Press, 1996

[15] Temam R. Navier-Stokes Equations. Amsterdam: North Holland, 1979

[16] Damlamian A, Miara B, Li Tatsien, eds. Multiscale Problems: Theory, Numerical Approximation and Applications. Beijing: High Education Press, 2011

[17] Yao Z A. Homogenization of some linear and semi-linear Schr¨odinger equations with real potential. Acta Math Sci, 2001, 21B(1): 137–144

[18] Yao Z A, Zhao H X. Homogenization of a stationary Navier-Stokes flow in porous medium with thin film. Acta Math Sci, 2008, 28B(4): 963–974