Localisation de la vorticité et applications au comportement asymptotique des solutions de Navier-Stokes
Brandolese, Lorenzo
Journées équations aux dérivées partielles, (2002), p. 1-14 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

Nous présentons quelques résultats de localisation, en variables d’espace, temps et fréquence, pour la vorticité associée aux écoulements dans ℝ 3 d’un fluide visqueux. Nous étudions, ensuite, la localisation des écoulements caractérisés par des fortes oscillations de la vorticité.

We study the localization, with respect to the space, time and frequency variables, of the vorticity of a viscous flow filling the whole space. The special behavior of flows with highly oscillating vorticity is also discussed.

Publié le : 2002-01-01
DOI : https://doi.org/10.5802/jedp.601 
@article{JEDP_2002____A3_0,
     author = {Brandolese, Lorenzo},
     title = {Localisation de la vorticit\'e et applications au comportement asymptotique des solutions de Navier-Stokes},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {2002},
     pages = {1-14},
     doi = {10.5802/jedp.601},
     mrnumber = {1968199},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/JEDP_2002____A3_0}
}

Brandolese, Lorenzo. Localisation de la vorticité et applications au comportement asymptotique des solutions de Navier-Stokes. Journées équations aux dérivées partielles,  (2002), pp. 1-14. doi : 10.5802/jedp.601. http://gdmltest.u-ga.fr/item/JEDP_2002____A3_0/

[Bra01] L. Brandolese, On the Localization of Symmetric and Asymmetric Solutions of the Navier-Stokes Equations dans R n, C. R. Acad. Sci. Paris, t. 332, Série I, 125-130 (2001). III-13 | MR 1813769 | Zbl 0973.35149

[Bra02] L. Brandolese Asymptotic behavior of the energy and pointwise estimates for solutions to the Navier-Stokes equations, prépublication.

[Da] R. Danchin, Analyse numérique et harmonique d'un problème de mécanique des fluides, Thèse de doctorat, École Polytechnique, Palaiseau, France, Décembre (1996).

[DS] Dobrokhotov S. Y., Shafarevich, A. I., Some Integral Identities and Remarks on the Decay at Infinity of the Solutions to the Navier-Stokes Equations in the Entire Space, Russ. J. Math. Phys. Vol. 2, N. 1 (1994) 133-135 | MR 1297948 | Zbl 0976.35508

[GM] Y. Giga, T. Miyakawa, Navier-Stokes Flow in R 3 with Measures as Initial Vorticity and Morrey Spaces, Commun. in Partial Diff. Equations, 14, 5, 577- 618, (1989). | MR 993821 | Zbl 0681.35072

[GW] T. Gallay, C. E. Wayne, Long-time asymptotics of the Navier-Stokes and vorticity equations on R 3, prépublication, Univ. Orsay (2001). | MR 1949968

[Ka84] T. Kato, Strong L p -solutions of the Navier-Stokes equations in R m, with applications to weak solutions, Math. Zeit. 187, 471-480 (1984). | MR 760047 | Zbl 0545.35073

[LT] Lu Ting, On the application of the integral invariants and decay laws of vorticity distributions, J. Fluid Mech. 127, 497-506 (1983). | MR 698525 | Zbl 0528.76034

[Mi] T. Miyakawa, On space time decay properties of nonstationary incompressible Navier-Stokes flows in R n, Funkcial. Ekvac., 32, N. 2, 541-557 (2000). | MR 1815476 | Zbl 02112739

[Sch] M. E. Schonbek, Lower Bounds of Rates of Decay for Solutions to the NavierStokes Equations, J. of the Amer. Math. Soc., 4, N. 3, 423-449 (1991). | MR 1103459 | Zbl 0739.35070

[Wie] M. Wiegner, Decay Results for Weak Solutions of the Navier-Stokes Equations on R n, J. London Math. Soc., 2, N. 35, 303-313 (1987) | MR 881519 | Zbl 0652.35095