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

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

  • Diego Chamorro

    Université d'Évry Val d'Essonne, Evry, France
  • Pierre Gilles Lemarié-Rieusset

    Université d'Évry Val d'Essonne, Evry, France
Quasi-geostrophic equations, nonlinear Bernstein inequalities and $\alpha$-stable processes cover
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Abstract

We prove some functional inequalities for the fractional differentiation operator (Δ)α(-\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.

Cite this article

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

DOI 10.4171/RMI/705