no. 1
A Stochastic Lagrangian Proof of Global Existence of the Navier-Stokes Equations for Flows With Small Reynolds Number
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 1, pp. 181-189 
@article{AIHPC_2009__26_1_181_0,
     author = {Iyer, Gautam},
     title = {A {Stochastic} {Lagrangian} {Proof} of {Global} {Existence} of the {Navier-Stokes} {Equations} for {Flows} {With} {Small} {Reynolds} {Number}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {181--189},
     year = {2009},
     publisher = {Elsevier},
     volume = {26},
     number = {1},
     doi = {10.1016/j.anihpc.2007.10.003},
     mrnumber = {2483818},
     zbl = {1156.76019},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2007.10.003/}
}
TY  - JOUR
AU  - Iyer, Gautam
TI  - A Stochastic Lagrangian Proof of Global Existence of the Navier-Stokes Equations for Flows With Small Reynolds Number
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2009
SP  - 181
EP  - 189
VL  - 26
IS  - 1
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.anihpc.2007.10.003/
DO  - 10.1016/j.anihpc.2007.10.003
LA  - en
ID  - AIHPC_2009__26_1_181_0
ER  - 
%0 Journal Article
%A Iyer, Gautam
%T A Stochastic Lagrangian Proof of Global Existence of the Navier-Stokes Equations for Flows With Small Reynolds Number
%J Annales de l'I.H.P. Analyse non linéaire
%D 2009
%P 181-189
%V 26
%N 1
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpc.2007.10.003/
%R 10.1016/j.anihpc.2007.10.003
%G en
%F AIHPC_2009__26_1_181_0
Iyer, Gautam. A Stochastic Lagrangian Proof of Global Existence of the Navier-Stokes Equations for Flows With Small Reynolds Number. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 1, pp. 181-189. doi: 10.1016/j.anihpc.2007.10.003

[1] Calderón A. P., Zygmund A., Singular Integrals and Periodic Functions, Studia Math. 14 (1954) 249-271, (1955). | Zbl | MR

[2] Chorin A. J., Marsden J. E., A Mathematical Introduction to Fluid Mechanics, Texts in Applied Mathematics, vol. 4, third ed., Springer-Verlag, New York, 1993. | Zbl

[3] Constantin P., Foias C., Navier-Stokes Equations, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1988. | Zbl | MR

[4] Constantin P., An Eulerian-Lagrangian Approach for Incompressible Fluids: Local Theory, J. Amer. Math. Soc. 14 (2) (2001) 263-278, (electronic). | Zbl | MR

[5] Constantin P., Iyer G., A Stochastic Lagrangian Representation of the 3-Dimensional Incompressible Navier-Stokes Equations, Comm. Pure Appl. Math. (2006), in press, available at, arXiv:math.PR/0511067. | Zbl

[6] Constantin P., Iyer G., Stochastic Lagrangian Transport and Generalized Relative Entropies, Commun. Math. Sci. 4 (4) (2006) 767-777. | Zbl | MR

[7] Constantin P., Kiselev A., Ryzhik L., Zlatoŝ A., Diffusion and Mixing in Fluid Flow, Ann. Math. (2006), in press, available at arXiv:, math.AP/0509663. | Zbl | MR

[8] Kato T., Fujita H., On the Nonstationary Navier-Stokes System, Rend. Sem. Mat. Univ. Padova 32 (1962) 243-260. | Zbl | MR | Numdam

[9] Fannjiang A., Kiselev A., Ryzhik L., Quenching of Reaction by Cellular Flows, Geom. Funct. Anal. 16 (1) (2006) 40-69. | Zbl | MR

[10] Fefferman C. L., Existence and Smoothness of the Navier-Stokes Equation, in: The Millennium Prize Problems, Clay Math. Inst., Cambridge, MA, 2006, pp. 57-67. | MR

[11] Freidlin M., Functional Integration and Partial Differential Equations, Annals of Mathematics Studies, vol. 109, Princeton University Press, Princeton, NJ, 1985. | Zbl | MR

[12] Friedman A., Stochastic Differential Equations and Applications. Vol. 1, Probability and Mathematical Statistics, vol. 28, Academic Press Harcourt Brace Jovanovich Publishers, New York, 1975. | Zbl | MR

[13] Gallagher I., Chemin J.-Y., On the Global Wellposedness of the 3-D Navier-Stokes Equations With Large Initial Data, Preprint, available at arXiv:, math.AP/0508374. | MR

[14] Iyer G., A Stochastic Perturbation of Inviscid Flows, Commun. Math. Phys. 266 (3) (2006) 631-645, available at arXiv:, math.AP/0505066. | Zbl | MR

[15] G. Iyer, A stochastic Lagrangian formulation of the Navier-Stokes and related transport equations, Ph.D. Thesis, University of Chicago, 2006.

[16] Karatzas I., Shreve S. E., Brownian Motion and Stochastic Calculus, Graduate Texts in Mathematics, vol. 113, second ed., Springer-Verlag, New York, 1991. | Zbl | MR

[17] Koch H., Tataru D., Well-Posedness for the Navier-Stokes Equations, Adv. Math. 157 (1) (2001) 22-35. | Zbl | MR

[18] Krylov N. V., Lectures on Elliptic and Parabolic Equations in Hölder Spaces, Graduate Studies in Mathematics, vol. 12, American Mathematical Society, Providence, RI, 1996. | Zbl | MR

[19] Krylov N. V., Rozovskiĭ B. L., Stochastic Partial Differential Equations and Diffusion Processes, Uspekhi Mat. Nauk 37 (6(228)) (1982) 75-95, (in Russian). | Zbl | MR

[20] Kunita H., Stochastic Flows and Stochastic Differential Equations, Cambridge Studies in Advanced Mathematics, vol. 24, Cambridge University Press, Cambridge, 1997, Reprint of the 1990 original. | Zbl | MR

[21] Rozovskiĭ B. L., Stochastic Evolution Systems: Linear Theory and Applications to Nonlinear Filtering, Mathematics and its Applications (Soviet Series), vol. 35, Kluwer Academic Publishers Group, Dordrecht, 1990, Translated from the Russian by A. Yarkho. | Zbl | MR

[22] Stein E. M., Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, vol. 30, Princeton University Press, Princeton, NJ, 1970. | Zbl | MR

Cité par Sources :