Global regularity of solutions of coupled Navier-stokes equations and nonlinear Fokker planck equations

Discrete and Continuous Dynamical Systems

Volumn 26, Issue 4, 2010, Pages 1185-1196

  Constantin, Peter ^a   Seregin, Gregory ^b  

^a UNIVERSITY OF CHICAGO   (United States)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Global existence; Navier stokes equations; Nonlinear Fokker Planck equations

Indexed keywords

EID: 77950277727     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2010.26.1185     Document Type: Article

References (14)

1. J. Bergh and J. Löfstrom, "Interpolation Spaces, an Introduction," Grundlehren der Mathematischen Wissenschaften, No.223, Springer-Verlag, Berlin-New York, 1976.
2. P. Constantin, Nonlinear Fokker-Planck Navier-Stokes systems, Commun. Math. Sci., 3 (2005), 531-544.
3. P. Constantin, Smoluchowski Navier-Stokes systems, Stochastic analysis and partial differential equations, 85-109, Contemp. Math., 429,
4. Amer. Math. Soc., Providence, RI, (2007).
5. P. Constantin, C. Fefferman, E. Titi and A. Zarnescu, Regularity for coupled two-dimensional nonlinear Fokker-Planck and Navier-Stokes systems, Commun. Math. Phys., 270 (2007) 789-811.
6. P. Constantin and N. Masmoudi, Global well-posedness for a Smoluchowski equation coupled with Navier-Stokes equations in 2D, Commun. Math. Phys., 278 (2008), 179-191.
7. P. Constantin and G. Seregin, Holder continuity of solutions of 2D Navier-Stokes equations with singular forcing, preprint.
8. M. Doi and S. F. Edwards, "The Theory of Polymer Dynamics," Oxford University Press, Oxford, 1988.
9. O. A. Ladyzhenskaya, Global solvability of a boundary value roblem for the Navier-Stokes equations in the case of two spatial variables, Doklady of the USSR, 123 (1958), 427-429.
10. P. G. Lemarié-Rieusset, "Recent Developments in the Navier-Stokes Problem," Chapmann and HaU/CRC, Research Notes in Mathematics, 431, Chapman & Hall/CRC, Boca Raton, FL, 2002.
11. C. LeBris and P-L. Lions, Existence and uniqueness of solutions to Fokker-Planck type equations with irregular coefficients, Commun. PDE, 33 (2008), 1272-1317.
12. Z. Lei, N. Masmoudi and Y. Zhou, Remarks on the blowup criteria for Oldroyd models, to appear.
13. F. Lin, P. Zhang and Z. Zhang, On the global existence of smooth solution to the 2D FENE dumbell model, Commun. Math. Phys., 277 (2008), 531-553.
14. N. Masmoudi, P. Zhang and Z. Zhang, Global well-posedness for 2D polymeric fluid models and growth estimate, Phys. D, 237 (2008), 1663-1675.