A regularity criterion for the 3D NSE in a local version of the space of functions of bounded mean oscillations
Grujić, Zoran ; Guberović, Rafaela
Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010), p. 773-778 / Harvested from Numdam
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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},
     volume = {27},
     year = {2010},
     pages = {773-778},
     doi = {10.1016/j.anihpc.2009.11.009},
     mrnumber = {2595201},
     zbl = {1187.35153},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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) pp. 773-778. doi : 10.1016/j.anihpc.2009.11.009. http://gdmltest.u-ga.fr/item/AIHPC_2010__27_2_773_0/

[1] J.T. Beale, T. Kato, A. Majda, Remarks on the breakdown of smooth solutions for the 3-D Euler equations, Comm. Math. Phys. 94 (1984), 61-66 | MR 763762 | Zbl 0573.76029

[2] L. Caffarelli, R. Kohn, L. Nirenberg, Partial regularity of suitable weak solutions of the Navier–Stokes equations, Comm. Pure Appl. Math. 35 (1982), 771-831 | MR 673830 | Zbl 0509.35067

[3] D. Chae, K. Kang, J. Lee, Notes on the asymptotically self-similar singularities in the Euler and the Navier–Stokes equations, Discrete Contin. Dyn. Syst. 25 (2009), 1181-1193 | MR 2552134 | Zbl 1179.35208

[4] D.-C. Chang, The dual of Hardy spaces on a bounded domain in ℝ n , Forum Math. 6 (1994), 65-81 | MR 1253178 | Zbl 0803.42014

[5] R. Coifman, P.-L. Lions, Y. Meyer, S. Semmes, Compensated compactness and Hardy spaces, J. Math. Pures Appl. 72 (1993), 247-286 | MR 1225511 | Zbl 0864.42009

[6] R. Coifman, Y. Meyer, Au dela des operateurs pseudodifferentieles, Astérisque 57 (1978) | Zbl 0483.35082

[7] P. Constantin, Navier–Stokes equations and area of interfaces, Comm. Math. Phys. 129 (1990), 241-266 | MR 1048693 | Zbl 0725.35080

[8] C. Fefferman, E.M. Stein, H p spaces of several variables, Acta Math. 129 (1972), 137-193 | MR 447953 | Zbl 0257.46078

[9] D. Goldberg, A local version of real Hardy spaces, Duke Math. J. 46 (1979), 27-42 | MR 523600 | Zbl 0409.46060

[10] Z. Grujić, Localization and geometric depletion of vortex-stretching in the 3D NSE, Comm. Math. Phys. 290 (2009), 861-870 | MR 2525642 | Zbl 1184.35240

[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 2669442

[12] Z. Grujić, Qi S. Zhang, 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 2202302 | Zbl 1106.35048

[13] H. Kozono, Y. Taniuchi, Bilinear estimates in BMO and the Navier–Stokes equations, Math. Z. 235 (2000), 173-194 | MR 1785078 | Zbl 0970.35099

[14] H. Kozono, T. Ogawa, Y. Taniuchi, The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations, Math. Z. 242 (2002), 251-278 | MR 1980623 | Zbl 1055.35087

[15] H. Kozono, T. Ogawa, Y. Taniuchi, Navier–Stokes equations in the Besov space near L ∞ and BMO, Kyushu J. Math. 57 (2003), 303-324 | MR 2050088 | Zbl 1067.35064