Une localisation spatio-temporelle de la version BMO du critère de Beale–Kato–Majda pour la régularité des solutions des équations de Navier–Stokes obtenue par Kozono et Taniuchi, c.-à-d., l'intégrabilité en temps de la norme BMO de la vorticité, est présentée.
A spatio-temporal localization of the BMO-version of the Beale–Kato–Majda criterion for the regularity of solutions to the 3D Navier–Stokes equations obtained by Kozono and Taniuchi, i.e., the time-integrability of the BMO-norm of the vorticity, is presented.
@article{AIHPC_2010__27_2_773_0, author = {Gruji\'c, Zoran and Guberovi\'c, Rafaela}, title = {A regularity criterion for the {3D} {NSE} in a local version of the space of functions of bounded mean oscillations}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {773--778}, publisher = {Elsevier}, volume = {27}, number = {2}, year = {2010}, doi = {10.1016/j.anihpc.2009.11.009}, mrnumber = {2595201}, zbl = {1187.35153}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2009.11.009/} }
TY - JOUR AU - Grujić, Zoran AU - Guberović, Rafaela TI - A regularity criterion for the 3D NSE in a local version of the space of functions of bounded mean oscillations JO - Annales de l'I.H.P. Analyse non linéaire PY - 2010 SP - 773 EP - 778 VL - 27 IS - 2 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2009.11.009/ DO - 10.1016/j.anihpc.2009.11.009 LA - en ID - AIHPC_2010__27_2_773_0 ER -
%0 Journal Article %A Grujić, Zoran %A Guberović, Rafaela %T A regularity criterion for the 3D NSE in a local version of the space of functions of bounded mean oscillations %J Annales de l'I.H.P. Analyse non linéaire %D 2010 %P 773-778 %V 27 %N 2 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2009.11.009/ %R 10.1016/j.anihpc.2009.11.009 %G en %F AIHPC_2010__27_2_773_0
Grujić, Zoran; Guberović, Rafaela. A regularity criterion for the 3D NSE in a local version of the space of functions of bounded mean oscillations. Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 2, pp. 773-778. doi : 10.1016/j.anihpc.2009.11.009. http://archive.numdam.org/articles/10.1016/j.anihpc.2009.11.009/
[1] Remarks on the breakdown of smooth solutions for the 3-D Euler equations, Comm. Math. Phys. 94 (1984), 61-66 | MR | Zbl
, , ,[2] Partial regularity of suitable weak solutions of the Navier–Stokes equations, Comm. Pure Appl. Math. 35 (1982), 771-831 | MR | Zbl
, , ,[3] Notes on the asymptotically self-similar singularities in the Euler and the Navier–Stokes equations, Discrete Contin. Dyn. Syst. 25 (2009), 1181-1193 | MR | Zbl
, , ,[4] The dual of Hardy spaces on a bounded domain in , Forum Math. 6 (1994), 65-81 | EuDML | MR | Zbl
,[5] Compensated compactness and Hardy spaces, J. Math. Pures Appl. 72 (1993), 247-286 | MR | Zbl
, , , ,[6] Au dela des operateurs pseudodifferentieles, Astérisque 57 (1978) | Numdam | Zbl
, ,[7] Navier–Stokes equations and area of interfaces, Comm. Math. Phys. 129 (1990), 241-266 | MR | Zbl
,[8] spaces of several variables, Acta Math. 129 (1972), 137-193 | MR | Zbl
, ,[9] A local version of real Hardy spaces, Duke Math. J. 46 (1979), 27-42 | MR | Zbl
,[10] Localization and geometric depletion of vortex-stretching in the 3D NSE, Comm. Math. Phys. 290 (2009), 861-870 | MR | Zbl
,[11] Z. Grujić, R. Guberović, Localization of the analytic regularity criteria on the vorticity and balance between the vorticity magnitude and coherence of the vorticity direction in the 3D NSE, Comm. Math. Phys., in press | MR
[12] Space–time localization of a class of geometric criteria for preventing blow-up in the 3D NSE, Comm. Math. Phys. 262 (2006), 555-564 | MR | Zbl
, ,[13] Bilinear estimates in BMO and the Navier–Stokes equations, Math. Z. 235 (2000), 173-194 | MR | Zbl
, ,[14] The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations, Math. Z. 242 (2002), 251-278 | MR | Zbl
, , ,[15] Navier–Stokes equations in the Besov space near and BMO, Kyushu J. Math. 57 (2003), 303-324 | MR | Zbl
, , ,Cité par Sources :