Revista Matemática Iberoamericana


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Volume 28, Issue 4, 2012, pp. 1109–1122
DOI: 10.4171/RMI/705

Published online: 2012-10-14

Quasi-geostrophic equations, nonlinear Bernstein inequalities and $\alpha$-stable processes

Diego Chamorro[1] and Pierre Gilles Lemarié-Rieusset[2]

(1) Université d'Évry Val d'Essonne, Evry, France
(2) Université d'Évry Val d'Essonne, Evry, France

We prove some functional inequalities for the fractional differentiation operator $(-\Delta)^\alpha$ through the formalism of semi-groups. This gives us an estimate of the regularity of Marchand’s weak solutions for the dissipative quasi-geostrophic equation.

Keywords: Besov spaces, semi-groups, Bernstein inequalities, quasi-geostrophic equation, stratified Lie groups, $\alpha$-stable processes

Chamorro Diego, Lemarié-Rieusset Pierre Gilles: Quasi-geostrophic equations, nonlinear Bernstein inequalities and $\alpha$-stable processes. Rev. Mat. Iberoamericana 28 (2012), 1109-1122. doi: 10.4171/RMI/705