-
Previous Article
The moving boundary problem in a chemotaxis model
- CPAA Home
- This Issue
-
Next Article
Global solutions to the incompressible magnetohydrodynamic equations
On the regularity of solutions to the Navier-Stokes equations
| 1. | Politecnico di Milano - Dipartimento di Matematica "F. Brioschi", Via Bonardi 9, 20133 Milano |
References:
| [1] |
H. Beirão da Veiga, Remarks on the smoothness of the $L^\infty(0,T;L^3)$ solutions of the 3-D Navier-Stokes equations,, Portugal. Math., 54 (1997), 381.
|
| [2] |
C. Bjorland and A. Vasseur, Weak in space, log in time improvement of the Ladyž zenskaja-Prodi-Serrin criteria,, J. Math. Fluid Mech., (). |
| [3] |
C. H. Chan and A. Vasseur, Log improvement of the Prodi-Serrin criteria for Navier-Stokes equations,, Methods Appl. Anal., 14 (2007), 197.
|
| [4] |
L. Escauriaza, G. Seregin and V. Šverák, $L_{3,\infty}$ -solutions of the Navier-Stokes equations and backward uniqueness,, Russian Math. Surveys, 58 (2003), 211.
|
| [5] |
C. Foias, C. Guillope and R. Temam, New a priori estimates for Navier-Stokes equations in dimension 3,, Comm. Partial Differential Equations, 6 (1981), 329.
|
| [6] |
E. Hopf, Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen,, Math. Nachr., 4 (1950), 213.
|
| [7] |
Y. Giga, Solutions for semilinear parabolic equations in $L^p$ and regularity of weak solutions of the Navier-Stokes equations,, J. Differential Equations, 62 (1986), 186.
|
| [8] |
J. Leray, Sur le mouvement d'un liquide visqueux emplissant l'espace,, Acta Math., 63 (1934), 193.
|
| [9] |
S. Montgomery-Smith, Conditions implying regularity of the three dimensional Navier-Stokes equation,, Appl. Math., 50 (2005), 451.
|
| [10] |
J. Nečas, M. Ruzička and V. Šverák, On Leray's self-similar solutions of the Navier-Stokes equations,, Acta Math., 176 (1996), 283.
|
| [11] |
G. Prodi, Un teorema di unicità per le equazioni di Navier-Stokes,, Ann. Mat. Pura Appl., 48 (1959), 173.
|
| [12] |
J. Serrin, On the interior regularity of weak solutions of the Navier-Stokes equations,, Arch. Ration. Mech. Anal., 9 (1962), 187.
|
| [13] |
H. Sohr, A regularity class for the Navier-Stokes equations in Lorentz spaces,, J. Evol. Equ., 1 (2001), 441.
|
| [14] |
H. Sohr, "The Navier-Stokes Euations,", Birkh\, (2001).
|
| [15] |
M. Struwe, On partial regularity results for the Navier-Stokes equations,, Comm. Pure Appl. Math., 41 (1988), 437.
|
| [16] |
S. Takahashi, On interior regularity criteria for weak solutions of the Navier-Stokes equations,, Manuscripta Math., 69 (1990), 237.
|
| [17] |
G. Talenti, Best constant in Sobolev inequality,, Ann. Mat. Pura Appl., 110 (1976), 353.
|
| [18] |
R. Temam, "Navier-Stokes Equations and Nonlinear Functional Analysis,", CBMS-NSF Regional conference Series in Applied Mathematics, (1983).
|
| [19] |
R. Temam, "Navier-Stokes Equations,", AMS Chelsea Publishing, (2001).
|
show all references
References:
| [1] |
H. Beirão da Veiga, Remarks on the smoothness of the $L^\infty(0,T;L^3)$ solutions of the 3-D Navier-Stokes equations,, Portugal. Math., 54 (1997), 381.
|
| [2] |
C. Bjorland and A. Vasseur, Weak in space, log in time improvement of the Ladyž zenskaja-Prodi-Serrin criteria,, J. Math. Fluid Mech., (). |
| [3] |
C. H. Chan and A. Vasseur, Log improvement of the Prodi-Serrin criteria for Navier-Stokes equations,, Methods Appl. Anal., 14 (2007), 197.
|
| [4] |
L. Escauriaza, G. Seregin and V. Šverák, $L_{3,\infty}$ -solutions of the Navier-Stokes equations and backward uniqueness,, Russian Math. Surveys, 58 (2003), 211.
|
| [5] |
C. Foias, C. Guillope and R. Temam, New a priori estimates for Navier-Stokes equations in dimension 3,, Comm. Partial Differential Equations, 6 (1981), 329.
|
| [6] |
E. Hopf, Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen,, Math. Nachr., 4 (1950), 213.
|
| [7] |
Y. Giga, Solutions for semilinear parabolic equations in $L^p$ and regularity of weak solutions of the Navier-Stokes equations,, J. Differential Equations, 62 (1986), 186.
|
| [8] |
J. Leray, Sur le mouvement d'un liquide visqueux emplissant l'espace,, Acta Math., 63 (1934), 193.
|
| [9] |
S. Montgomery-Smith, Conditions implying regularity of the three dimensional Navier-Stokes equation,, Appl. Math., 50 (2005), 451.
|
| [10] |
J. Nečas, M. Ruzička and V. Šverák, On Leray's self-similar solutions of the Navier-Stokes equations,, Acta Math., 176 (1996), 283.
|
| [11] |
G. Prodi, Un teorema di unicità per le equazioni di Navier-Stokes,, Ann. Mat. Pura Appl., 48 (1959), 173.
|
| [12] |
J. Serrin, On the interior regularity of weak solutions of the Navier-Stokes equations,, Arch. Ration. Mech. Anal., 9 (1962), 187.
|
| [13] |
H. Sohr, A regularity class for the Navier-Stokes equations in Lorentz spaces,, J. Evol. Equ., 1 (2001), 441.
|
| [14] |
H. Sohr, "The Navier-Stokes Euations,", Birkh\, (2001).
|
| [15] |
M. Struwe, On partial regularity results for the Navier-Stokes equations,, Comm. Pure Appl. Math., 41 (1988), 437.
|
| [16] |
S. Takahashi, On interior regularity criteria for weak solutions of the Navier-Stokes equations,, Manuscripta Math., 69 (1990), 237.
|
| [17] |
G. Talenti, Best constant in Sobolev inequality,, Ann. Mat. Pura Appl., 110 (1976), 353.
|
| [18] |
R. Temam, "Navier-Stokes Equations and Nonlinear Functional Analysis,", CBMS-NSF Regional conference Series in Applied Mathematics, (1983).
|
| [19] |
R. Temam, "Navier-Stokes Equations,", AMS Chelsea Publishing, (2001).
|
| [1] |
Reinhard Farwig, Paul Felix Riechwald. Regularity criteria for weak solutions of the Navier-Stokes system in general unbounded domains. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 157-172. doi: 10.3934/dcdss.2016.9.157 |
| [2] |
Thomas Y. Hou, Ruo Li. Nonexistence of locally self-similar blow-up for the 3D incompressible Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2007, 18 (4) : 637-642. doi: 10.3934/dcds.2007.18.637 |
| [3] |
Jochen Merker. Strong solutions of doubly nonlinear Navier-Stokes equations. Conference Publications, 2011, 2011 (Special) : 1052-1060. doi: 10.3934/proc.2011.2011.1052 |
| [4] |
Peter E. Kloeden, José Valero. The Kneser property of the weak solutions of the three dimensional Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2010, 28 (1) : 161-179. doi: 10.3934/dcds.2010.28.161 |
| [5] |
Yukang Chen, Changhua Wei. Partial regularity of solutions to the fractional Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5309-5322. doi: 10.3934/dcds.2016033 |
| [6] |
Jishan Fan, Yasuhide Fukumoto, Yong Zhou. Logarithmically improved regularity criteria for the generalized Navier-Stokes and related equations. Kinetic & Related Models, 2013, 6 (3) : 545-556. doi: 10.3934/krm.2013.6.545 |
| [7] |
Zijin Li, Xinghong Pan. Some Remarks on regularity criteria of Axially symmetric Navier-Stokes equations. Communications on Pure & Applied Analysis, 2019, 18 (3) : 1333-1350. doi: 10.3934/cpaa.2019064 |
| [8] |
Baoquan Yuan, Xiao Li. Blow-up criteria of smooth solutions to the three-dimensional micropolar fluid equations in Besov space. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 2167-2179. doi: 10.3934/dcdss.2016090 |
| [9] |
Hamid Bellout, Jiří Neustupa, Patrick Penel. On a $\nu$-continuous family of strong solutions to the Euler or Navier-Stokes equations with the Navier-Type boundary condition. Discrete & Continuous Dynamical Systems - A, 2010, 27 (4) : 1353-1373. doi: 10.3934/dcds.2010.27.1353 |
| [10] |
Yinghua Li, Shijin Ding, Mingxia Huang. Blow-up criterion for an incompressible Navier-Stokes/Allen-Cahn system with different densities. Discrete & Continuous Dynamical Systems - B, 2016, 21 (5) : 1507-1523. doi: 10.3934/dcdsb.2016009 |
| [11] |
Michele Campiti, Giovanni P. Galdi, Matthias Hieber. Global existence of strong solutions for $2$-dimensional Navier-Stokes equations on exterior domains with growing data at infinity. Communications on Pure & Applied Analysis, 2014, 13 (4) : 1613-1627. doi: 10.3934/cpaa.2014.13.1613 |
| [12] |
Peter Constantin, Gregory Seregin. Global regularity of solutions of coupled Navier-Stokes equations and nonlinear Fokker Planck equations. Discrete & Continuous Dynamical Systems - A, 2010, 26 (4) : 1185-1196. doi: 10.3934/dcds.2010.26.1185 |
| [13] |
Daniel Coutand, J. Peirce, Steve Shkoller. Global well-posedness of weak solutions for the Lagrangian averaged Navier-Stokes equations on bounded domains. Communications on Pure & Applied Analysis, 2002, 1 (1) : 35-50. doi: 10.3934/cpaa.2002.1.35 |
| [14] |
Fang Li, Bo You, Yao Xu. Dynamics of weak solutions for the three dimensional Navier-Stokes equations with nonlinear damping. Discrete & Continuous Dynamical Systems - B, 2018, 23 (10) : 4267-4284. doi: 10.3934/dcdsb.2018137 |
| [15] |
Daniel Pardo, José Valero, Ángel Giménez. Global attractors for weak solutions of the three-dimensional Navier-Stokes equations with damping. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 1-22. doi: 10.3934/dcdsb.2018279 |
| [16] |
Zoran Grujić. Regularity of forward-in-time self-similar solutions to the 3D Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2006, 14 (4) : 837-843. doi: 10.3934/dcds.2006.14.837 |
| [17] |
Wendong Wang, Liqun Zhang, Zhifei Zhang. On the interior regularity criteria of the 3-D navier-stokes equations involving two velocity components. Discrete & Continuous Dynamical Systems - A, 2018, 38 (5) : 2609-2627. doi: 10.3934/dcds.2018110 |
| [18] |
Huyuan Chen, Hichem Hajaiej, Ying Wang. Boundary blow-up solutions to fractional elliptic equations in a measure framework. Discrete & Continuous Dynamical Systems - A, 2016, 36 (4) : 1881-1903. doi: 10.3934/dcds.2016.36.1881 |
| [19] |
Zhifu Xie. General uniqueness results and examples for blow-up solutions of elliptic equations. Conference Publications, 2009, 2009 (Special) : 828-837. doi: 10.3934/proc.2009.2009.828 |
| [20] |
Jacek Banasiak. Blow-up of solutions to some coagulation and fragmentation equations with growth. Conference Publications, 2011, 2011 (Special) : 126-134. doi: 10.3934/proc.2011.2011.126 |
2018 Impact Factor: 0.925
Tools
Metrics
Other articles
by authors
[Back to Top]