@article{AIHPC_2009__26_6_2165_0, author = {Chen, Qionglei and Miao, Changxing and Zhang, Zhifei}, title = {On the {Uniqueness} of {Weak} {Solutions} for the {3D} {Navier-Stokes} {Equations}}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {2165--2180}, publisher = {Elsevier}, volume = {26}, number = {6}, year = {2009}, doi = {10.1016/j.anihpc.2009.01.008}, mrnumber = {2569890}, zbl = {1260.35106}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2009.01.008/} }
TY - JOUR AU - Chen, Qionglei AU - Miao, Changxing AU - Zhang, Zhifei TI - On the Uniqueness of Weak Solutions for the 3D Navier-Stokes Equations JO - Annales de l'I.H.P. Analyse non linéaire PY - 2009 SP - 2165 EP - 2180 VL - 26 IS - 6 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2009.01.008/ DO - 10.1016/j.anihpc.2009.01.008 LA - en ID - AIHPC_2009__26_6_2165_0 ER -
%0 Journal Article %A Chen, Qionglei %A Miao, Changxing %A Zhang, Zhifei %T On the Uniqueness of Weak Solutions for the 3D Navier-Stokes Equations %J Annales de l'I.H.P. Analyse non linéaire %D 2009 %P 2165-2180 %V 26 %N 6 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2009.01.008/ %R 10.1016/j.anihpc.2009.01.008 %G en %F AIHPC_2009__26_6_2165_0
Chen, Qionglei; Miao, Changxing; Zhang, Zhifei. On the Uniqueness of Weak Solutions for the 3D Navier-Stokes Equations. Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 6, pp. 2165-2180. doi : 10.1016/j.anihpc.2009.01.008. http://archive.numdam.org/articles/10.1016/j.anihpc.2009.01.008/
[1] A New Regularity Class for the Navier-Stokes Equations in , Chinese Ann. Math. Ser. B 16 (1995) 407-412. | MR | Zbl
,[2] Calcul Symbolique Et Propagation Des Singularités Pour Les Équations Aux Dérivées Partielles Non Linéaires, Ann. Sci. École Norm. Sup. 14 (1981) 209-246. | Numdam | MR | Zbl
,[3] A Losing Estimate for the Ideal MHD Equations With Application to Blow-Up Criterion, SIAM J. Math. Anal. 38 (2007) 1847-1859. | MR | Zbl
, , ,[4] Space-Time Estimates in the Besov Spaces and the Navier-Stokes Equations, Methods Appl. Anal. 13 (2006) 107-122. | MR
, ,[5] Perfect Incompressible Fluids, Oxford University Press, New York, 1998. | MR | Zbl
,[6] Théorèmes D'unicité Pour Le Système De Navier-Stokes Tridimensionnel, J. Anal. Math. 77 (1999) 27-50. | MR | Zbl
,[7] Flot De Champs De Vecteurs Non Lipschitziens Et Équations De Navier-Stokes, J. Differential Equations 121 (1995) 314-328. | MR | Zbl
, ,[8] On the Regularity of Weak Solutions of the 3D Navier-Stokes Equations in , arXiv:0708.3067v2[math.AP]. | MR
, ,[9] Estimates in Besov Spaces for Transport and Transport-Diffusion Equations With Almost Lipschitz Coefficients, Rev. Mat. Iberoamericana 21 (2005) 863-888. | MR | Zbl
,[10] Le Théorème De Leray Et Le Théorème De Fujita-Kato Pour Le Système De Boussinesq Partiellement Visqueux, Bulletin de la Societe Mathematique de France 136 (2008) 261-309. | Numdam | MR | Zbl
, ,[11] -Solutions to the Navier-Stokes Equations and Backward Uniqueness, Russian Math. Surveys 58 (2003) 211-250. | MR | Zbl
, , ,[12] On Global Infinite Energy Solutions to the Navier-Stokes Equations in Two Dimensions, Arch. Ration. Mech. Anal. 161 (2002) 307-337. | MR | Zbl
, ,[13] Multipliers, Paramultipliers, and Weak-Strong Uniqueness for the Navier-Stokes Equations, J. Differential Equations 226 (2006) 373-428. | MR | Zbl
,[14] Solutions for Semilinear Parabolic Equations in and Regularity of Weak Solutions of the Navier-Stokes System, J. Differential Equations 62 (1986) 186-212. | MR | Zbl
,[15] Remark on Uniqueness of Weak Solutions to the Navier-Stokes Equations, Analysis 16 (1996) 255-271. | MR | Zbl
, ,[16] Bilinear Estimates in BMO and the Navier-Stokes Equations, Math. Z. 235 (2000) 173-194. | MR | Zbl
, ,[17] The Critical Sobolev Inequalities in Besov Spaces and Regularity Criterion to Some Semi-Linear Evolution Equations, Math. Z. 242 (2002) 251-278. | MR | Zbl
, , ,[18] Bilinear Estimates in Homogeneous Triebel-Lizorkin Spaces and the Navier-Stokes Equations, Math. Nachr. 276 (2004) 63-74. | MR | Zbl
, ,[19] Recent Developments in the Navier-Stokes Problem, Res. Notes Math., vol. 43, Chapman and Hall/CRC, 2002. | MR | Zbl
,[20] Uniqueness for the Navier-Stokes Problem: Remarks on a Theorem of Jean-Yves Chemin, Nonlinearity 20 (2007) 1475-1490. | MR | Zbl
,[21] Sur Le Mouvement D'un Liquids Visqeux Emplissant L'espace, Acta Math. 63 (1934) 193-248. | JFM | MR
,[22] On the Global Existence of Smooth Solution to the 2-D FENE Dumbbell Model, Comm. Math. Phys. 277 (2008) 531-553. | MR | Zbl
, , ,[23] Vorticity and Incompressible Flow, Cambridge University Press, Cambridge, 2002. | MR | Zbl
, ,[24] Global Well-Posedness for 2D Polymeric Fluid Models and Growth Estimate, Physica D 237 (2008) 1663-1675. | MR | Zbl
, , ,[25] Un Teorema Di Unicità Per Le Equazioni Di Navier-Stokes, Ann. Mat. Pura Appl. 48 (1959) 173-182. | MR | Zbl
,[26] A Remark on the Uniqueness Problem for the Weak Solutions of Navier-Stokes Equations, Ann. Fac. Sci. Toulouse Math. 11 (2002) 225-238. | Numdam | MR | Zbl
,[27] The Initial Value Problem for the Navier-Stokes Equations, in: (Ed.), Nonlinear Problems, University of Wisconsin Press, Madison, 1963, pp. 69-98. | MR | Zbl
,[28] Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, NJ, 1993. | MR | Zbl
,[29] Theory of Function Spaces, Monogr. Math., vol. 78, Birkhäuser-Verlag, Basel, 1983. | MR | Zbl
,Cited by Sources: