American Institute of Mathematical Sciences

Advanced
January  2000, 6(1): 191-210. doi: 10.3934/dcds.2000.6.191

Renormalization group method: Application to Navier-Stokes equation

I. Moise 1, and  Roger Temam 2,

1. 

The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, Indiana 47405, United States
2. 

The Institute for Scientific Computing and Applied Mathematics, Indiana University, 831 E. 3rd St., Rawles Hall, Bloomington, IN 47405

Received  October 1999 Published  December 1999

The aim of this article is to present a rather unusual and partly heuristic application of the renormalization group (RG) theory to the Navier-Stokes equations with space periodic boundary conditions. We obtain in this way a new nonlinear renormalized equation with a nonlinear term which is invariant under the Stokes operator. Its relation to the Navier-Stokes equations is investigated for non-resonant domains.
Keywords: Renormalization group method, Galerkin method., Navier­Stokes equations.
Mathematics Subject Classification: 35Q10, 35Q30, 76D05, 35B20. .
Citation: I. Moise, Roger Temam. Renormalization group method: Application to Navier-Stokes equation. Discrete & Continuous Dynamical Systems, 2000, 6 (1) : 191-210. doi: 10.3934/dcds.2000.6.191
[1]

Yinnian He, R. M.M. Mattheij. Reformed post-processing Galerkin method for the Navier-Stokes equations. Discrete & Continuous Dynamical Systems - B, 2007, 8 (2) : 369-387. doi: 10.3934/dcdsb.2007.8.369
[2]

Kaitai Li, Yanren Hou. Fourier nonlinear Galerkin method for Navier-Stokes equations. Discrete & Continuous Dynamical Systems, 1996, 2 (4) : 497-524. doi: 10.3934/dcds.1996.2.497
[3]

Hui Peng, Qilong Zhai. Weak Galerkin method for the Stokes equations with damping. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021112
[4]

Evrad M. D. Ngom, Abdou Sène, Daniel Y. Le Roux. Boundary stabilization of the Navier-Stokes equations with feedback controller via a Galerkin method. Evolution Equations & Control Theory, 2014, 3 (1) : 147-166. doi: 10.3934/eect.2014.3.147
[5]

Kaifang Liu, Lunji Song, Shan Zhao. A new over-penalized weak galerkin method. Part Ⅰ: Second-order elliptic problems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2411-2428. doi: 10.3934/dcdsb.2020184
[6]

Lunji Song, Wenya Qi, Kaifang Liu, Qingxian Gu. A new over-penalized weak galerkin finite element method. Part Ⅱ: Elliptic interface problems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2581-2598. doi: 10.3934/dcdsb.2020196
[7]

Nathan Glatt-Holtz, Mohammed Ziane. Singular perturbation systems with stochastic forcing and the renormalization group method. Discrete & Continuous Dynamical Systems, 2010, 26 (4) : 1241-1268. doi: 10.3934/dcds.2010.26.1241
[8]

Hi Jun Choe, Hyea Hyun Kim, Do Wan Kim, Yongsik Kim. Meshless method for the stationary incompressible Navier-Stokes equations. Discrete & Continuous Dynamical Systems - B, 2001, 1 (4) : 495-526. doi: 10.3934/dcdsb.2001.1.495
[9]

Hi Jun Choe, Do Wan Kim, Yongsik Kim. Meshfree method for the non-stationary incompressible Navier-Stokes equations. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 17-39. doi: 10.3934/dcdsb.2006.6.17
[10]

Takayuki Kubo, Ranmaru Matsui. On pressure stabilization method for nonstationary Navier-Stokes equations. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2283-2307. doi: 10.3934/cpaa.2018109
[11]

Ben-Yu Guo, Yu-Jian Jiao. Mixed generalized Laguerre-Fourier spectral method for exterior problem of Navier-Stokes equations. Discrete & Continuous Dynamical Systems - B, 2009, 11 (2) : 315-345. doi: 10.3934/dcdsb.2009.11.315
[12]

Yueqiang Shang, Qihui Zhang. A subgrid stabilizing postprocessed mixed finite element method for the time-dependent Navier-Stokes equations. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3119-3142. doi: 10.3934/dcdsb.2020222
[13]

Corrado Falcolini, Laura Tedeschini-Lalli. A numerical renormalization method for quasi–conservative periodic attractors. Journal of Computational Dynamics, 2020, 7 (2) : 461-468. doi: 10.3934/jcd.2020018
[14]

Zhendong Luo. A reduced-order SMFVE extrapolation algorithm based on POD technique and CN method for the non-stationary Navier-Stokes equations. Discrete & Continuous Dynamical Systems - B, 2015, 20 (4) : 1189-1212. doi: 10.3934/dcdsb.2015.20.1189
[15]

Mikhail Dokuchaev, Guanglu Zhou, Song Wang. A modification of Galerkin's method for option pricing. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021077
[16]

Yoshifumi Aimoto, Takayasu Matsuo, Yuto Miyatake. A local discontinuous Galerkin method based on variational structure. Discrete & Continuous Dynamical Systems - S, 2015, 8 (5) : 817-832. doi: 10.3934/dcdss.2015.8.817
[17]

Vladislav Balashov, Alexander Zlotnik. An energy dissipative semi-discrete finite-difference method on staggered meshes for the 3D compressible isothermal Navier–Stokes–Cahn–Hilliard equations. Journal of Computational Dynamics, 2020, 7 (2) : 291-312. doi: 10.3934/jcd.2020012
[18]

Netra Khanal, Ramjee Sharma, Jiahong Wu, Juan-Ming Yuan. A dual-Petrov-Galerkin method for extended fifth-order Korteweg-de Vries type equations. Conference Publications, 2009, 2009 (Special) : 442-450. doi: 10.3934/proc.2009.2009.442
[19]

Juan-Ming Yuan, Jiahong Wu. A dual-Petrov-Galerkin method for two integrable fifth-order KdV type equations. Discrete & Continuous Dynamical Systems, 2010, 26 (4) : 1525-1536. doi: 10.3934/dcds.2010.26.1525
[20]

Yanzhao Cao, Li Yin. Spectral Galerkin method for stochastic wave equations driven by space-time white noise. Communications on Pure & Applied Analysis, 2007, 6 (3) : 607-617. doi: 10.3934/cpaa.2007.6.607

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (141)
  • HTML views (0)
  • Cited by (16)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences