Regularity of Coupled Two-Dimensional Nonlinear Fokker-Planck and Navier-Stokes Systems
- First Online:
- 249 Downloads
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.
Unable to display preview. Download preview PDF.
- 2.Chemin, J.Y.: Perfect Incompressible Fluids. Oxford Lecture Series in Mathematics and its Applications. 14, New York: Clarendon Press Oxford University Press, 1998Google Scholar
- 6.Doi M. and Edwards S.F. (1988). The Theory of Polymer Dynamics. Oxford University Press, Oxford Google Scholar
- 8.Helgason, S.: Differential Geometry, Lie Groups and Symmetric spaces. London Academic Press, 1978Google Scholar
- 9.Hörmander, L.: The Analysis of Linear Partial Differential Operators. Vol. 3, Berlin-Heidelberg- New York-Tokyo: Springer-Verlag 1985Google Scholar
- 12.Lemarié-Rieusset, P.G.: Recent Developments in the Navier-Stokes Problem. Chapmann and Hall/CRC Research Notes in Mathematics 431, Boca Raton, FL: CRC, 2002Google Scholar
- 16.Otto, F., Tzavaras, A.: Continuity of velocity gradients in suspensions of rod-like molecules. SFB Preprint 147 (2004), available at http://www.math.Umd.edu/Ntzavaras/reprints/existence.pdfGoogle Scholar