Dissipative Quasi-Geostrophic Equations with Lp Data
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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.
CitationWu, J. (2001). Dissipative quasi-geostrophic equations with Lp data. Electronic Journal of Differential Equations, 2001(56), pp. 1-13.
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