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Global well-posedness for the critical 2D dissipative quasi-geostrophic equation. (English) Zbl 1121.35115
A proof of the global well-posedness for the two-dimensional dissipative quasi-geostrophic equation is presented. The argument relies on a non-local maximum principle.

35Q35PDEs in connection with fluid mechanics
76U05Rotating fluids
86A05Hydrology, hydrography, oceanography
Full Text: DOI arXiv
[1] Caffarelli, L., Vasseur, A.: Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Preprint, math.AP/0608447 · Zbl 1204.35063
[2] Constantin, P.: Energy spectrum of quasigeostrophic turbulence. Phys. Rev. Lett. 89, 184501 (2002) · doi:10.1103/PhysRevLett.89.184501
[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)
[4] Constantin, P., Majda, A., Tabak, E.: Formation of strong fronts in the 2D quasi-geostrophic thermal active scalar. Nonlinearity 7, 1495--1533 (1994) · Zbl 0809.35057 · doi:10.1088/0951-7715/7/6/001
[5] Constantin, P., Wu, J.: Behavior of solutions of 2D quasi-geostrophic equations. SIAM J. Math. Anal. 30, 937--948 (1999) · Zbl 0957.76093 · doi:10.1137/S0036141098337333
[6] Cordoba, A., Cordoba, D.: A maximum principle applied to quasi-geostrophic equations. Commun. Math. Phys. 249, 511--528 (2004) · Zbl 1309.76026 · doi:10.1007/s00220-004-1055-1
[7] Kiselev, A., Nazarov, F., Shterenberg, R.: On blow up and regularity in dissipative Burgers equation. In preparation · Zbl 1186.35020
[8] Resnick, S.: Dynamical problems in nonlinear advective partial differential equations. Ph.D. Thesis, University of Chicago, 1995
[9] Wu, J.: The quasi-geostrophic equation and its two regularizations. Commun. Partial Differ. Equations 27, 1161--1181 (2002) · Zbl 1012.35067 · doi:10.1081/PDE-120004898