Communications in Mathematical Physics

, Volume 270, Issue 3, pp 789–811

Regularity of Coupled Two-Dimensional Nonlinear Fokker-Planck and Navier-Stokes Systems


    • Department of MathematicsThe University of Chicago
  • C. Fefferman
    • Department of Mathematics, Princeton University
  • E. S. Titi
    • Department of Mathematics and Department of Mechanics and Aerospace EngineeringUniversity of California
    • Department of Computer Science and Applied MathematicsWeizmann Institute of Science
  • A. Zarnescu
    • Department of MathematicsThe University of Chicago

DOI: 10.1007/s00220-006-0183-1

Cite this article as:
Constantin, P., Fefferman, C., Titi, E.S. et al. Commun. Math. Phys. (2007) 270: 789. doi:10.1007/s00220-006-0183-1


We consider systems of particles coupled with fluids. The particles are described by the evolution of their density, and the fluid is described by the Navier-Stokes equations. The particles add stress to the fluid and the fluid carries and deforms the particles. Because the particles perform rapid random motion, we assume that the density of particles is carried by a time average of the fluid velocity. The resulting coupled system is shown to have smooth solutions at all values of parameters, in two spatial dimensions.

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© Springer-Verlag 2006