Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 56, pp. 1-13.

Title: Dissipative quasi-geostrophic equations with $L^p$ data
   
Author: Jiahong Wu (Oklahoma State Univ., Stillwater, OK , USA)

Abstract:  
 We seek solutions of the initial value  problem for the 
 2D dissipative quasi-geostrophic (QG) equation with $L^p$ 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 $L^p$ 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.