Electron. J. Diff. Eqns., Vol. 2001(2001), No. 56, pp. 1-13.

Dissipative quasi-geostrophic equations with Lp data

Jiahong Wu

We seek solutions of the initial value problem for the 2D dissipative quasi-geostrophic (QG) equation with Lp initial data. The 2D dissipative QG equation is a two dimensional model of the 3D incompressible Navier-Stokes equations. We prove global existence and uniqueness of regular solutions for the dissipative QG equation with sub-critical powers. For the QG equation with critical or super-critical powers, we establish explicit global Lp bounds for its solutions and conclude that any possible finite time singularity must occur in the first order derivative.

Submitted June 18, 2001. Published August 3, 2001.
Math Subject Classifications: 35Q35, 76U05, 86A10.
Key Words: 2D quasi-geostrophic equation, initial-value problem, existence, uniqueness.

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Jiahong Wu
Department of Mathematics
Oklahoma State University
401 Mathematical Sciences
Stillwater, OK 74078 USA
e-mail: jiahong@math.okstate.edu

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