Geodesic
Dissipative quasi-geostrophic equations with \(L^p\) data
Electronic journal of differential equations, Tome 2001 (2001)
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.
Classification : 35Q35, 76U05, 86A10
Keywords: 2D quasi-geostrophic equation, initial-value problem, existence, uniqueness 
@article{EJDE_2001__2001__a48,
     author = {Wu,  Jiahong},
     title = {Dissipative quasi-geostrophic equations with {\(L^p\)} data},
     journal = {Electronic journal of differential equations},
     year = {2001},
     volume = {2001},
     zbl = {0987.35127},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a48/}
}
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%A Wu,  Jiahong
%T Dissipative quasi-geostrophic equations with \(L^p\) data
%J Electronic journal of differential equations
%D 2001
%V 2001
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%F EJDE_2001__2001__a48
Wu,  Jiahong. Dissipative quasi-geostrophic equations with \(L^p\) data. Electronic journal of differential equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a48/