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

Diego Chamorro; Pierre Gilles Lemarié-Rieusset

doi:10.4171/rmi/705

JournalsrmiVol. 28, No. 4pp. 1109–1122

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

Diego Chamorro
Université d'Évry Val d'Essonne, Evry, France
Pierre Gilles Lemarié-Rieusset
Université d'Évry Val d'Essonne, Evry, France
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Abstract

We prove some functional inequalities for the fractional differentiation operator $(- Δ)^{α}$ 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.

Cite this article

Diego Chamorro, Pierre Gilles Lemarié-Rieusset, Quasi-geostrophic equations, nonlinear Bernstein inequalities and $α$ -stable processes. Rev. Mat. Iberoam. 28 (2012), no. 4, pp. 1109–1122

DOI 10.4171/RMI/705