Circulation and Energy Theorem Preserving Stochastic Fluids

Leray, J.: Sur les movements d’un fluide visqueux remplaissant l’espace, Acta Math. 63, 193 (1934)

1934

Earlier work this paper cites.

Kraichnan, R. H. and Nagarajan, S.: Growth of turbulent magnetic fields, Phys. Fluids 10 859–870 (1967)

1967

Earlier work this paper cites.

Kazantsev, A. P.,: Enhancement of a magnetic field by a conducting fluid, Sov. Phys. JETP 26 1031–1034 (1968)

1968

Earlier work this paper cites.

Kraichnan, R. H.: Small-scale structure of a scalar field convected by turbulence, Phys. Fluids 11 945–953 (1968)

1968

Earlier work this paper cites.

Krylov, N. V., and Rozovskii, B.L.: Stochastic evolution equations. Itogi Nauki i Tekhniki. Seriya “Sovremennye Problemy Matematiki. Noveishie Dostizheniya” 14 (1979): 71–146

1979

Earlier work this paper cites.

Kunita, H.: Some extensions of Ito’s formula. Séminaire de Probabilités XV 1979/80. Springer, Berlin, Heidelberg, 1981. 118–141

1981

Earlier work this paper cites.

Le Jan, Y., and Watanabe, S.: Stochastic flows of diffeomorphisms. North-Holland Mathematical Library. Vol. 32. Elsevier, 1984. 307-332

1984

Earlier work this paper cites.

Constantin, P., and Foias, C. (1988). Navier-stokes equations. University of Chicago Press

1988

Earlier work this paper cites.

Marsden, J. E., and Hughes, T. J. (1994). Mathematical Foundations of Elasticity. Courier Corporation

1994

Earlier work this paper cites.

Flandoli, F., Gatarek, D.: Martingale and stationary solutions for stochastic Navier–Stokes equations, Probab. Theory Related Fields 102 (1995), no. 3, 367–391

1995

Earlier work this paper cites.

Kunita, H.: Stochastic Flows and Stochastic Differential Equations, Cambridge Studies in Advanced Mathematics, vol. 24. Cambridge, UK: Cambridge Univ. Press (1997)

1997

Earlier work this paper cites.

Holm, D. D., Marsden, J. E. and Ratiu, T. S.: The Euler–Poincaré equations and semidirect products with applications to continuum theories, Adv. in Math. 137 (1998): 1-81

1998

Earlier work this paper cites.

Arnold, V. I., and Khesin, B. A. Topological methods in hydrodynamics Springer. New York, (1998)

1998

Earlier work this paper cites.

Holm, D. D., Marsden, J. E., and Ratiu, T. S.: Euler-Poincaré models of ideal fluids with nonlinear dispersion. Phys. Rev. Lett. 349, 4173-4177, (1998)

1998

Earlier work this paper cites.

Chen, S., Foias, C., Holm, D. D., Olson, E. J., Titi, E. S. and Wynne, S.: The Camassa-Holm equations as a closure model for turbulent channel and pipe flows, Phys. Rev. Lett., 81, 5338-5341 (1998)

1998

Earlier work this paper cites.

Bernard, D., Gawedzki, K., and Kupiainen, A.: Slow modes in passive advection. J. Stat, Phys. 90.3-4 (1998): 519-569

1998

Earlier work this paper cites.

Arnold, V I., and Khesin, B.A.: Topological methods in hydrodynamics. Vol. 125. Springer Science & Business Media, 1999

1999

Cited alongside, same era.

Constantin, P.: An Euler–Lagrangian approach for incompressible fluids: local theory. J. Amer. Math. Soc. 14 (2001), 263–27

2001

Cited alongside, same era.

Foias, C., Holm, D. D., and Titi, E. S.: The Navier-Stokes–alpha model of fluid turbulence, Physica D, 152-153, 505-519 (2001)

2001

Cited alongside, same era.

Foias, C., Holm, D. D., and Titi, E. S.: The three dimensional viscous Camassa-Holm equations, and their relation to the Navier-Stokes equations and turbulence theory. J. Dyn. and Diff. Eqns. 14, 1-35 (2002)

2002

Cited alongside, same era.

Geurts, B. J. and Holm, D. D.: Alpha-modeling strategy for LES of turbulent mixing. In Turbulent Flow Computation

2002

Cited alongside, same era.

Constantin, P., and Iyer, G.: A stochastic-Lagrangian approach to the Navier–Stokes equations in domains with boundary. Annals Appl. Prob. 21, no. 4 (2011): 1466-1492

2011

Later among the works it cites.

Flandoli, F.: Random Perturbation of PDEs and Fluid Dynamic Models: École d’été de Probabilités de Saint-Flour XL 2010. Vol. 2015. Springer Science & Business Media, 2011

2011

Later among the works it cites.

Mémin, E.: Fluid flow dynamics under location uncertainty. Geophys. Astrophys. Fluid Dyn., 108 (2014), no. 2, 119–146

2014

Later among the works it cites.

Holm, D. D.: Variational principles for stochastic fluid dynamics. Proc. R. Soc. A 471.2176 (2015): 20140963

2015

Later among the works it cites.

Crisan, D., Franco F., and Holm, D. D.: Solution properties of a 3D stochastic Euler fluid equation. arXiv preprint arXiv:1704.06989 (2017)

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