Equations de Navier-Stokes dans le plan avec tourbillon initial mesure

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1. M. Ben-Artzi. Global solutions of two-dimensional Navier-Stokes and Euler equations. Arch. Rational Mech. Anal.128, 329–358, 1994. Zbl0837.35110MR1308857
2. H. Brezis. Remarks on the preceding paper by M. Ben-Artzi : “Global solutions of two-dimensional Navier-Stokes and Euler equations”. Arch. Rational Mech. Anal., 128, 359–360, 1994. Zbl0837.35112
3. M. Cannone et F. Planchon. Self-similar solutions for Navier-Stokes equations in ${ℝ}^3$. Commun. Partial Differ. Equations, 21, 179–193, 1996. Zbl0842.35075MR1373769
4. E. A. Carlen et M. Loss. Optimal smoothing and decay estimates for viscously damped conservation laws, with applications to the $2$-D Navier-Stokes equation. Duke Math. J., 81, 135–157 (1996), 1995. Zbl0859.35011MR1381974
5. A. Carpio. Asymptotic behavior for the vorticity equations in dimensions two and three. Comm. Partial Differential Equations, 19, 827–872, 1994. Zbl0816.35108MR1274542
6. G.-H. Cottet. Équations de Navier-Stokes dans le plan avec tourbillon initial mesure. C. R. Acad. Sci. Paris Sér. I Math., 303, 105–108, 1986. Zbl0606.35065MR853597
7. I. Gallagher et Th. Gallay. Uniqueness of the solutions of the Navier-Stokes equation in ${ℝ}^2$ with measure-valued initial vorticity. Article en préparation, 2004. 
8. Th. Gallay et C. E. Wayne. Invariant manifolds and the long-time asymptotics of the Navier-Stokes and vorticity equations on ${ℝ}^2$. Arch. Ration. Mech. Anal., 163, 209–258, 2002. Zbl1042.37058MR1912106
9. Th. Gallay et C. E. Wayne. Long-time asymptotics of the Navier-Stokes and vorticity equations on ${ℝ}^3$. R. Soc. Lond. Philos. Trans. Ser. A Math. Phys. Eng. Sci., 360, 2155–2188, 2002. Recent developments in the mathematical theory of water waves (Oberwolfach, 2001). Zbl1048.35055MR1949968
10. Th. Gallay. Tourbillon d’Oseen et comportement asymptotique des solutions de l’équation de Navier-Stokes. Séminaire EDP de l’Ecole Polytechnique 2001-2002, exposé ${\mathrm{n}}^{\mathrm{o}}$V. 
11. Th. Gallay et C.E. Wayne. Global stability of vortex solutions of the two-dimensional Navier-Stokes equation. Prépublication de l’Institut Fourier (2003), disponible sur http://arXiv.org/abs/math/0402449. Zbl1139.35084
12. M.-H. Giga et Y. Giga. Nonlinear partial differential equations : asymptotic behaviour of solutions and self-similar solutions. Ouvrage publié en japonais en 1999, traduction anglaise en préparation, 2004. 
13. Y. Giga et T. Kambe. Large time behavior of the vorticity of two-dimensional viscous flow and its application to vortex formation. Comm. Math. Phys., 117, 549–568, 1988. Zbl0661.76018MR953819
14. Y. Giga, T. Miyakawa, et H. Osada. Two-dimensional Navier-Stokes flow with measures as initial vorticity. Arch. Rational Mech. Anal., 104, 223–250, 1988. Zbl0666.76052MR1017289
15. S. Kamin (Kamenomostskaya). The asymptotic behavior of the solution of the filtration equation. Israel J. Math., 14, 76–87, 1973. Zbl0254.35054MR315292
16. T. Kato. The Navier-Stokes equation for an incompressible fluid in ${ℝ}^2$ with a measure as the initial vorticity. Differential Integral Equations, 7, 949–966, 1994. Zbl0826.35094MR1270113
17. J. Leray. Etude de diverses équations intégrales non linéaires et de quelques problèmes que pose l’hydrodynamique. J. Math. Pures. Appl., 12, 1–82, 1933. Zbl0006.16702
18. H. Osada. Diffusion processes with generators of generalized divergence form. J. Math. Kyoto Univ., 27, 597–619, 1987. Zbl0657.35073MR916761
19. A. Prochazka et D. I. Pullin. On the two-dimensional stability of the axisymmetric Burgers vortex. Phys. Fluids, 7, 1788–1790, 1995. Zbl1023.76546MR1336103
20. L. Rossi et J. Graham-Eagle. On the existence of two-dimensional, localized, rotating, self-similar vortical structures. SIAM J. Appl. Math., 62, 2114–2128, 2002. Zbl1010.35083MR1918309

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