218 research outputs found
Regularity of H\"older continuous solutions of the supercritical quasi-geostrophic equation
We present a regularity result for weak solutions of the 2D quasi-geostrophic
equation with supercritical () dissipation : If
a Leray-Hopf weak solution is H\"{o}lder continuous with on the time interval , then it is actually a classical solution on
A new Bernstein's Inequality and the 2D Dissipative Quasi-Geostrophic Equation
We show a new Bernstein's inequality which generalizes the results of
Cannone-Planchon, Danchin and Lemari\'{e}-Rieusset. As an application of this
inequality, we prove the global well-posedness of the 2D quasi-geostrophic
equation with the critical and super-critical dissipation for the small initial
data in the critical Besov space, and local well-posedness for the large
initial data.Comment: 18page
On the global well-posedness of the critical quasi-geostrophic equation
We prove the global well-posedness of the critical dissipative
quasi-geostrophic equation for large initial data belonging to the critical
Besov space $\dot B^0_{\infty,1}(\RR^2).
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