Communications in Mathematical Physics

, Volume 270, Issue 3, pp 789–811 | Cite as

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

  • P. Constantin
  • C. Fefferman
  • E. S. Titi
  • A. Zarnescu


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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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • P. Constantin
    • 1
  • C. Fefferman
    • 2
  • E. S. Titi
    • 3
    • 4
  • A. Zarnescu
    • 1
  1. 1.Department of MathematicsThe University of ChicagoChicagoUSA
  2. 2.Department of Mathematics, Princeton UniversityPrincetonUSA
  3. 3.Department of Mathematics and Department of Mechanics and Aerospace EngineeringUniversity of CaliforniaIrvineUSA
  4. 4.Department of Computer Science and Applied MathematicsWeizmann Institute of ScienceRehovotIsrael

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