Oceanic and atmospheric dynamics are often interpreted through potential vorticity, as this
quantity is conserved along the geostrophic flow. However, in addition to potential vorticity …

Motivated by the critical dissipative quasi-geostrophic equation, we prove that drift-diffusion
equations with L² initial data and minimal assumptions on the drift are locally Hölder …

We study the initial value problem for dissipative 2D Quasi-geostrophic equations proving
local existence, global results for small initial data in the super-critical case, decay of L p …

Global well-posedness for the critical 2D dissipative quasi-geostrophic equation Page 1 DOI:
10.1007/s00222-006-0020-3 Invent. math. 167, 445–453 (2007) Global well-posedness for …

Euler equations of incompressible fluids use and enrich many branches of mathematics,
from integrable systems to geometric analysis. They present important open physical and …

In 2004 the mathematical world will mark 120 years since the advent of turbulence theory
([80]). In his 1884 paper Reynolds introduced the decomposition of turbulent flow into mean …

The long time behavior of the solutions to the two dimensional dissipative quasi-geostrophic
equations is studied. We obtain a new positivity lemma which improves a previous version of …

We study the two dimensional dissipative quasi-geostrophic equations in the Sobolev space
Existence and uniqueness of the solution local in time is proved in H s when s> 2 (1− α) …

This paper establishes several existence and uniqueness results for two families of active
scalar equations with velocity fields determined by the scalars through very singular …

We show a new Bernstein's inequality which generalizes the results of Cannone-Planchon,
Danchin and Lemarié-Rieusset. As an application of this inequality, we prove the global well …