@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}, publisher = {Elsevier}, volume = {26}, number = {1}, year = {2009}, doi = {10.1016/j.anihpc.2007.10.003}, mrnumber = {2483818}, zbl = {1156.76019}, language = {en}, url = {http://archive.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 - http://archive.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 http://archive.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, Volume 26 (2009) no. 1, pp. 181-189. doi : 10.1016/j.anihpc.2007.10.003. http://archive.numdam.org/articles/10.1016/j.anihpc.2007.10.003/
[1] Singular Integrals and Periodic Functions, Studia Math. 14 (1954) 249-271, (1955). | MR | Zbl
, ,[2] A Mathematical Introduction to Fluid Mechanics, Texts in Applied Mathematics, vol. 4, third ed., Springer-Verlag, New York, 1993. | Zbl
, ,[3] Navier-Stokes Equations, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1988. | MR | Zbl
, ,[4] An Eulerian-Lagrangian Approach for Incompressible Fluids: Local Theory, J. Amer. Math. Soc. 14 (2) (2001) 263-278, (electronic). | MR | Zbl
,[5] 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] Stochastic Lagrangian Transport and Generalized Relative Entropies, Commun. Math. Sci. 4 (4) (2006) 767-777. | MR | Zbl
, ,[7] Diffusion and Mixing in Fluid Flow, Ann. Math. (2006), in press, available at arXiv:, math.AP/0509663. | MR | Zbl
, , , ,[8] On the Nonstationary Navier-Stokes System, Rend. Sem. Mat. Univ. Padova 32 (1962) 243-260. | Numdam | MR | Zbl
, ,[9] Quenching of Reaction by Cellular Flows, Geom. Funct. Anal. 16 (1) (2006) 40-69. | MR | Zbl
, , ,[10] Existence and Smoothness of the Navier-Stokes Equation, in: The Millennium Prize Problems, Clay Math. Inst., Cambridge, MA, 2006, pp. 57-67. | MR
,[11] Functional Integration and Partial Differential Equations, Annals of Mathematics Studies, vol. 109, Princeton University Press, Princeton, NJ, 1985. | MR | Zbl
,[12] Stochastic Differential Equations and Applications. Vol. 1, Probability and Mathematical Statistics, vol. 28, Academic Press Harcourt Brace Jovanovich Publishers, New York, 1975. | MR | Zbl
,[13] On the Global Wellposedness of the 3-D Navier-Stokes Equations With Large Initial Data, Preprint, available at arXiv:, math.AP/0508374. | MR
, ,[14] A Stochastic Perturbation of Inviscid Flows, Commun. Math. Phys. 266 (3) (2006) 631-645, available at arXiv:, math.AP/0505066. | MR | Zbl
,[15] G. Iyer, A stochastic Lagrangian formulation of the Navier-Stokes and related transport equations, Ph.D. Thesis, University of Chicago, 2006.
[16] Brownian Motion and Stochastic Calculus, Graduate Texts in Mathematics, vol. 113, second ed., Springer-Verlag, New York, 1991. | MR | Zbl
, ,[17] Well-Posedness for the Navier-Stokes Equations, Adv. Math. 157 (1) (2001) 22-35. | MR | Zbl
, ,[18] Lectures on Elliptic and Parabolic Equations in Hölder Spaces, Graduate Studies in Mathematics, vol. 12, American Mathematical Society, Providence, RI, 1996. | MR | Zbl
,[19] Stochastic Partial Differential Equations and Diffusion Processes, Uspekhi Mat. Nauk 37 (6(228)) (1982) 75-95, (in Russian). | MR | Zbl
, ,[20] Stochastic Flows and Stochastic Differential Equations, Cambridge Studies in Advanced Mathematics, vol. 24, Cambridge University Press, Cambridge, 1997, Reprint of the 1990 original. | MR | Zbl
,[21] 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. | MR | Zbl
,[22] Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, vol. 30, Princeton University Press, Princeton, NJ, 1970. | MR | Zbl
,Cited by Sources: