Propagation of chaos for the 2D viscous vortex model
暂无分享,去创建一个
[1] H. Osada. A stochastic differential equation arising from the vortex problem , 1985 .
[2] H. Brezis. Remarks on the preceding paper by M. Ben-Artzi “Global solutions of two-dimensional Navier-Stokes and Euler equations” , 1994 .
[3] F. Malrieu. Convergence to equilibrium for granular media equations and their Euler schemes , 2003 .
[4] Freddy Bouchet,et al. Statistical mechanics of two-dimensional and geophysical flows , 2011, 1110.6245.
[5] L. Onsager,et al. Statistical hydrodynamics , 1949 .
[6] Camillo De Lellis,et al. Estimates and regularity results for the DiPerna-Lions flow , 2008 .
[7] S. Méléard. Asymptotic behaviour of some interacting particle systems; McKean-Vlasov and Boltzmann models , 1996 .
[8] Uniqueness for the two-dimensional Navier–Stokes equation with a measure as initial vorticity , 2004, math/0406297.
[9] Vladimir I. Clue. Harmonic analysis , 2004, 2004 IEEE Electro/Information Technology Conference.
[10] C. Marchioro. On the Inviscid Limit for a Fluid with a Concentrated Vorticity , 1998 .
[11] Shinzo Watanabe,et al. On the uniqueness of solutions of stochastic difierential equations , 1971 .
[12] Branching process associated with 2d-Navier Stokes equation , 2001 .
[13] C. Villani,et al. Entropy and chaos in the Kac model , 2008, 0808.3192.
[14] Leslie Greengard,et al. A fast algorithm for particle simulations , 1987 .
[15] P. Lions,et al. On the Fokker-Planck-Boltzmann equation , 1988 .
[16] Emmanuel Cépa,et al. Diffusing particles with electrostatic repulsion , 1997 .
[17] M. Ben-Artzi. Global solutions of two-dimensional Navier-Stokes and euler equations , 1994 .
[18] Mario Pulvirenti,et al. Mathematical Theory of Incompressible Nonviscous Fluids , 1993 .
[19] H. Osada. Limit Points of Empirical Distributions of Vorticies with Small Viscosity , 1987 .
[20] P. Lions,et al. Existence and Uniqueness of Solutions to Fokker–Planck Type Equations with Irregular Coefficients , 2008 .
[21] Global Stability of Vortex Solutions of the Two-Dimensional Navier-Stokes Equation , 2004, math/0402449.
[22] E. Carlen. Superadditivity of Fisher's information and logarithmic Sobolev inequalities , 1991 .
[23] M. Pulvirenti,et al. Hydrodynamics in two dimensions and vortex theory , 1982 .
[24] H. Helmholtz. Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen. , 1858 .
[25] St'ephane Mischler,et al. On Kac's chaos and related problems , 2014 .
[26] A. Sznitman. Topics in propagation of chaos , 1991 .
[27] S. Mischler,et al. A new approach to quantitative propagation of chaos for drift, diffusion and jump processes , 2011, 1101.4727.
[28] H. Osada. Diffusion processes with generators of generalized divergence form , 1987 .
[29] P. Lions,et al. A special class of stationary flows for two-dimensional euler equations: A statistical mechanics description. Part II , 1995 .
[30] L. J. Savage,et al. Symmetric measures on Cartesian products , 1955 .
[31] A. Sznitman. Équations de type de Boltzmann, spatialement homogènes , 1984 .
[32] A. Chorin. Numerical study of slightly viscous flow , 1973, Journal of Fluid Mechanics.
[33] Derek W. Robinson,et al. Mean entropy of states in classical statistical mechanics , 1967 .
[34] Steven Schochet,et al. THE POINT-VORTEX METHOD FOR PERIODIC WEAK SOLUTIONS OF THE 2-D EULER EQUATIONS , 1996 .
[35] Paths Clustering and an Existence Result for Stochastic Vortex Systems , 2007 .
[36] Arnaud Guillin,et al. Uniform Convergence to Equilibrium for Granular Media , 2012, 1204.4138.
[37] On the existence and uniqueness of SDE describing an $n$-particle system interacting via a singular potential , 1985 .
[38] M. Kac. Foundations of Kinetic Theory , 1956 .
[39] F. Flandoli,et al. Full well-posedness of point vortex dynamics corresponding to stochastic 2D Euler equations , 2010, 1004.1407.
[40] Sylvie Méléard,et al. Monte-Carlo approximations for 2d Navier-Stokes equations with measure initial data , 2001 .
[41] Alessio Figalli,et al. Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients , 2008 .
[42] T. Gallay. Interaction of Vortices in Weakly Viscous Planar Flows , 2009, 0908.2518.
[43] D. Aalto,et al. Maximal Functions in Sobolev Spaces , 2009 .
[44] H. Helson. Harmonic Analysis , 1983 .
[45] P. Lions,et al. Ordinary differential equations, transport theory and Sobolev spaces , 1989 .
[46] Hirofumi Osada,et al. Propagation of chaos for the two dimensional Navier-Stokes equation , 1986 .
[47] B. D. Finetti. La prévision : ses lois logiques, ses sources subjectives , 1937 .