Abstract
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.
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Caffarelli, L., Vasseur, A.: Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Preprint, math.AP/0608447
Constantin, P.: Energy spectrum of quasigeostrophic turbulence. Phys. Rev. Lett. 89, 184501 (2002)
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)
Constantin, P., Majda, A., Tabak, E.: Formation of strong fronts in the 2D quasi-geostrophic thermal active scalar. Nonlinearity 7, 1495–1533 (1994)
Constantin, P., Wu, J.: Behavior of solutions of 2D quasi-geostrophic equations. SIAM J. Math. Anal. 30, 937–948 (1999)
Cordoba, A., Cordoba, D.: A maximum principle applied to quasi-geostrophic equations. Commun. Math. Phys. 249, 511–528 (2004)
Kiselev, A., Nazarov, F., Shterenberg, R.: On blow up and regularity in dissipative Burgers equation. In preparation
Resnick, S.: Dynamical problems in nonlinear advective partial differential equations. Ph.D. Thesis, University of Chicago, 1995
Wu, J.: The quasi-geostrophic equation and its two regularizations. Commun. Partial Differ. Equations 27, 1161–1181 (2002)
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Mathematics Subject Classification (1991)
Primary: 35Q35; Secondary: 76U05
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Kiselev, A., Nazarov, F. & Volberg, A. Global well-posedness for the critical 2D dissipative quasi-geostrophic equation. Invent. math. 167, 445–453 (2007). https://doi.org/10.1007/s00222-006-0020-3
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DOI: https://doi.org/10.1007/s00222-006-0020-3