zbMATH — the first resource for mathematics

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.

35Q35 PDEs in connection with fluid mechanics
76U05 General theory of rotating fluids
86A05 Hydrology, 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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.