Inventiones mathematicae

, Volume 167, Issue 3, pp 445–453 | Cite as

Global well-posedness for the critical 2D dissipative quasi-geostrophic equation

  • A. Kiselev
  • F. Nazarov
  • A. Volberg


We give an elementary proof of the global well-posedness for the critical 2D dissipative quasi-geostrophic equation. The argument is based on a non-local maximum principle involving appropriate moduli of continuity.


Singular Integral Operator Dissipative Evolution Periodic Initial Data Thermal Active Scalar Unique Global Smooth Solution 
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  1. 1.
    Caffarelli, L., Vasseur, A.: Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Preprint, math.AP/0608447Google Scholar
  2. 2.
    Constantin, P.: Energy spectrum of quasigeostrophic turbulence. Phys. Rev. Lett. 89, 184501 (2002)CrossRefGoogle Scholar
  3. 3.
    Constantin, P., Cordoba, D., Wu, J.: On the critical dissipative quasi-geostrophic equation. Dedicated to Professors Ciprian Foias and Roger Temam (Bloomington, IN, 2000). Indiana Univ. Math. J. 50, 97–107 (2001)MathSciNetGoogle Scholar
  4. 4.
    Constantin, P., Majda, A., Tabak, E.: Formation of strong fronts in the 2D quasi-geostrophic thermal active scalar. Nonlinearity 7, 1495–1533 (1994)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Constantin, P., Wu, J.: Behavior of solutions of 2D quasi-geostrophic equations. SIAM J. Math. Anal. 30, 937–948 (1999)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Cordoba, A., Cordoba, D.: A maximum principle applied to quasi-geostrophic equations. Commun. Math. Phys. 249, 511–528 (2004)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Kiselev, A., Nazarov, F., Shterenberg, R.: On blow up and regularity in dissipative Burgers equation. In preparationGoogle Scholar
  8. 8.
    Resnick, S.: Dynamical problems in nonlinear advective partial differential equations. Ph.D. Thesis, University of Chicago, 1995Google Scholar
  9. 9.
    Wu, J.: The quasi-geostrophic equation and its two regularizations. Commun. Partial Differ. Equations 27, 1161–1181 (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA
  2. 2.Department of MathematicsMichigan State UniversityEast LansingUSA

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