Electron. J. Diff. Eqns., Vol. 2001(2001), No. 56, pp. 113.
Dissipative quasigeostrophic equations with
L^{p} data
Jiahong Wu
Abstract:
We seek solutions of the initial value problem for the
2D dissipative quasigeostrophic (QG) equation with
L^{p} initial data.
The 2D dissipative QG equation is a two dimensional model of the
3D incompressible NavierStokes equations.
We prove global existence and uniqueness of regular solutions for
the dissipative QG equation with subcritical powers.
For the QG equation with critical or supercritical 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 quasigeostrophic equation, initialvalue problem,
existence, uniqueness.
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Jiahong Wu
Department of Mathematics
Oklahoma State University
401 Mathematical Sciences
Stillwater, OK 74078 USA
email: jiahong@math.okstate.edu 
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