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The Kneser property of the weak solutions of the three dimensional Navier-Stokes equations
A mathematical and numerical study of incompressible flows with a surfactant monolayer
1. | Center for Computational Science, Tulane University, New Orleans, LA 70118, United States |
2. | Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907-2067 |
3. | Department of Mathematics, Purdue University, West Lafayette, IN 47907 |
[1] |
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 |
[2] |
Zhenhua Guo, Zilai Li. Global existence of weak solution to the free boundary problem for compressible Navier-Stokes. Kinetic and Related Models, 2016, 9 (1) : 75-103. doi: 10.3934/krm.2016.9.75 |
[3] |
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 |
[4] |
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 |
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Chérif Amrouche, María Ángeles Rodríguez-Bellido. On the very weak solution for the Oseen and Navier-Stokes equations. Discrete and Continuous Dynamical Systems - S, 2010, 3 (2) : 159-183. doi: 10.3934/dcdss.2010.3.159 |
[6] |
Qi S. Zhang. An example of large global smooth solution of 3 dimensional Navier-Stokes equations without pressure. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 5521-5523. doi: 10.3934/dcds.2013.33.5521 |
[7] |
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 |
[8] |
Hui Peng, Qilong Zhai. Weak Galerkin method for the Stokes equations with damping. Discrete and Continuous Dynamical Systems - B, 2022, 27 (4) : 1853-1875. doi: 10.3934/dcdsb.2021112 |
[9] |
Francesca Crispo, Paolo Maremonti. A remark on the partial regularity of a suitable weak solution to the Navier-Stokes Cauchy problem. Discrete and Continuous Dynamical Systems, 2017, 37 (3) : 1283-1294. doi: 10.3934/dcds.2017053 |
[10] |
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 |
[11] |
Chérif Amrouche, Nour El Houda Seloula. $L^p$-theory for the Navier-Stokes equations with pressure boundary conditions. Discrete and Continuous Dynamical Systems - S, 2013, 6 (5) : 1113-1137. doi: 10.3934/dcdss.2013.6.1113 |
[12] |
Lucas C. F. Ferreira, Elder J. Villamizar-Roa. On the existence of solutions for the Navier-Stokes system in a sum of weak-$L^{p}$ spaces. Discrete and Continuous Dynamical Systems, 2010, 27 (1) : 171-183. doi: 10.3934/dcds.2010.27.171 |
[13] |
Jingrui Wang, Keyan Wang. Almost sure existence of global weak solutions to the 3D incompressible Navier-Stokes equation. Discrete and Continuous Dynamical Systems, 2017, 37 (9) : 5003-5019. doi: 10.3934/dcds.2017215 |
[14] |
Jian-Guo Liu, Zhaoyun Zhang. Existence of global weak solutions of $ p $-Navier-Stokes equations. Discrete and Continuous Dynamical Systems - B, 2022, 27 (1) : 469-486. doi: 10.3934/dcdsb.2021051 |
[15] |
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 |
[16] |
Zhilei Liang, Jiangyu Shuai. Existence of strong solution for the Cauchy problem of fully compressible Navier-Stokes equations in two dimensions. Discrete and Continuous Dynamical Systems - B, 2021, 26 (10) : 5383-5405. doi: 10.3934/dcdsb.2020348 |
[17] |
Peter E. Kloeden, José Valero. The Kneser property of the weak solutions of the three dimensional Navier-Stokes equations. Discrete and Continuous Dynamical Systems, 2010, 28 (1) : 161-179. doi: 10.3934/dcds.2010.28.161 |
[18] |
Wenjing Song, Ganshan Yang. The regularization of solution for the coupled Navier-Stokes and Maxwell equations. Discrete and Continuous Dynamical Systems - S, 2016, 9 (6) : 2113-2127. doi: 10.3934/dcdss.2016087 |
[19] |
Atanas Stefanov. On the Lipschitzness of the solution map for the 2 D Navier-Stokes system. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 1471-1490. doi: 10.3934/dcds.2010.26.1471 |
[20] |
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 |
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