We prove some functional inequalities for the fractional differentiation operator 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.
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Diego Chamorro, Pierre Gilles Lemarié-Rieusset, Quasi-geostrophic equations, nonlinear Bernstein inequalities and -stable processes. Rev. Mat. Iberoam. 28 (2012), no. 4, pp. 1109–1122DOI 10.4171/RMI/705