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