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Propagation of Sobolev regularity for the critical dissipative quasi-geostrophic equation

Article type: Research Article

Authors: Marchand, Fabien

Affiliations: Université Paris Sud, Laboratoire de mathématiques, bât. 425, 91405 Orsay cedex, France E-mail: fabien.marchand@math.u-psud.fr

Abstract: We show that under a smallness assumption on the L∞ norm of the initial data, there is a propagation of any Sobolev regularity greater than −1/2 for some weak solutions of the critical dissipative quasi-geostrophic equation. We also prove the existence of solutions in a space close to the homogeneous Sobolev space $\dot{H}$1, theses solutions are given by a fixed point theorem.

Journal: Asymptotic Analysis, vol. 49, no. 3-4, pp. 275-293, 2006

Published: 2006
Price: EUR 27.50
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