American Institute of Mathematical Sciences

Advanced
2007, 2007(Special): 731-740. doi: 10.3934/proc.2007.2007.731

Navier-Stokes problems modeled by evolution hemivariational inequalities

Stanislaw Migórski 1, and  Anna Ochal 2,

1. 

Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Computer Science, ul. Nawojki 11, 30-072 Krakow
2. 

Jagiellonian University, Faculty of Mathematics and Computer Sciences, Institute of Computer Science, ul. Nawojki 11, 30-072 Krakow, Poland

Received  September 2006 Revised  February 2007 Published  September 2007

In this paper we study an inequality problem for the evolution Navier-Stokes type operators related to the model of motion of a viscous incompressible fluid in a bounded domain. The equations are nonlinear Navier-Stokes ones for the velocity and pressure with non-standard boundary conditions. We assume the nonslip boundary condition together with a Clarke subdifferential relation between the pressure and the normal components of the velocity. The existence of weak solutions to the model is proved by applying the regularized Galerkin method.
Keywords: Galerkin method, nonconvex, inclusion., Hemivariational inequality, subdifferential, Navier-Stokes equation.
Mathematics Subject Classification: Primary: 76D05, 47J20, 35K85, 74G25, 35Q30; Secondary: 35R70, 49J4.
Citation: Stanislaw Migórski, Anna Ochal. Navier-Stokes problems modeled by evolution hemivariational inequalities. Conference Publications, 2007, 2007 (Special) : 731-740. doi: 10.3934/proc.2007.2007.731
[1]

Yinnian He, R. M.M. Mattheij. Reformed post-processing Galerkin method for the Navier-Stokes equations. Discrete and 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 and Continuous Dynamical Systems, 1996, 2 (4) : 497-524. doi: 10.3934/dcds.1996.2.497
[3]

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 and Control Theory, 2014, 3 (1) : 147-166. doi: 10.3934/eect.2014.3.147
[4]

I. Moise, Roger Temam. Renormalization group method: Application to Navier-Stokes equation. Discrete and Continuous Dynamical Systems, 2000, 6 (1) : 191-210. doi: 10.3934/dcds.2000.6.191
[5]

Yinnian He, Kaitai Li. Nonlinear Galerkin approximation of the two dimensional exterior Navier-Stokes problem. Discrete and Continuous Dynamical Systems, 1996, 2 (4) : 467-482. doi: 10.3934/dcds.1996.2.467
[6]

G. M. de Araújo, S. B. de Menezes. On a variational inequality for the Navier-Stokes operator with variable viscosity. Communications on Pure and Applied Analysis, 2006, 5 (3) : 583-596. doi: 10.3934/cpaa.2006.5.583
[7]

Carlo Morosi, Livio Pizzocchero. On the constants in a Kato inequality for the Euler and Navier-Stokes equations. Communications on Pure and Applied Analysis, 2012, 11 (2) : 557-586. doi: 10.3934/cpaa.2012.11.557
[8]

Sun-Ho Choi. Weighted energy method and long wave short wave decomposition on the linearized compressible Navier-Stokes equation. Networks and Heterogeneous Media, 2013, 8 (2) : 465-479. doi: 10.3934/nhm.2013.8.465
[9]

Kuijie Li, Tohru Ozawa, Baoxiang Wang. Dynamical behavior for the solutions of the Navier-Stokes equation. Communications on Pure and Applied Analysis, 2018, 17 (4) : 1511-1560. doi: 10.3934/cpaa.2018073
[10]

C. Foias, M. S Jolly, I. Kukavica, E. S. Titi. The Lorenz equation as a metaphor for the Navier-Stokes equations. Discrete and Continuous Dynamical Systems, 2001, 7 (2) : 403-429. doi: 10.3934/dcds.2001.7.403
[11]

Bum Ja Jin, Kyungkeun Kang. Caccioppoli type inequality for non-Newtonian Stokes system and a local energy inequality of non-Newtonian Navier-Stokes equations without pressure. Discrete and Continuous Dynamical Systems, 2017, 37 (9) : 4815-4834. doi: 10.3934/dcds.2017207
[12]

Hi Jun Choe, Hyea Hyun Kim, Do Wan Kim, Yongsik Kim. Meshless method for the stationary incompressible Navier-Stokes equations. Discrete and Continuous Dynamical Systems - B, 2001, 1 (4) : 495-526. doi: 10.3934/dcdsb.2001.1.495
[13]

Hi Jun Choe, Do Wan Kim, Yongsik Kim. Meshfree method for the non-stationary incompressible Navier-Stokes equations. Discrete and Continuous Dynamical Systems - B, 2006, 6 (1) : 17-39. doi: 10.3934/dcdsb.2006.6.17
[14]

Takayuki Kubo, Ranmaru Matsui. On pressure stabilization method for nonstationary Navier-Stokes equations. Communications on Pure and Applied Analysis, 2018, 17 (6) : 2283-2307. doi: 10.3934/cpaa.2018109
[15]

Changjie Fang, Weimin Han. Stability analysis and optimal control of a stationary Stokes hemivariational inequality. Evolution Equations and Control Theory, 2020, 9 (4) : 995-1008. doi: 10.3934/eect.2020046
[16]

Igor Kukavica, Mohammed Ziane. Regularity of the Navier-Stokes equation in a thin periodic domain with large data. Discrete and Continuous Dynamical Systems, 2006, 16 (1) : 67-86. doi: 10.3934/dcds.2006.16.67
[17]

Imam Wijaya, Hirofumi Notsu. Stability estimates and a Lagrange-Galerkin scheme for a Navier-Stokes type model of flow in non-homogeneous porous media. Discrete and Continuous Dynamical Systems - S, 2021, 14 (3) : 1197-1212. doi: 10.3934/dcdss.2020234
[18]

Pavel I. Plotnikov, Jan Sokolowski. Compressible Navier-Stokes equations. Conference Publications, 2009, 2009 (Special) : 602-611. doi: 10.3934/proc.2009.2009.602
[19]

Jan W. Cholewa, Tomasz Dlotko. Fractional Navier-Stokes equations. Discrete and Continuous Dynamical Systems - B, 2018, 23 (8) : 2967-2988. doi: 10.3934/dcdsb.2017149
[20]

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

 Impact Factor: 

Tools

Metrics

  • PDF downloads (55)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy