We construct solutions in R 2 with finite energy of the surface quasi-geostrophic equations
(SQG) that initially are in C k (k≥ 2) but that are not in C k for t> 0. We prove a similar result …

We consider solutions to the generalized Surface Quasi-geostrophic equation (γ-SQG) when
the velocity is more singular than the active scalar function (ie γ∈(0, 1)). In this paper we …

We prove that the inviscid surface quasi-geostrophic (SQG) equations are strongly ill-posed
in critical Sobolev spaces: there exists an initial data $ H^{2}(\bbT^ 2) $ without any solutions …

In this paper, we are concerned with the long-time asymptotic behavior of the generalized
two-dimensional quasi-geostrophic equation. More precisely, we obtain the sharp time …

This paper studies the dissipative generalized surface quasi-geostrophic equations in a
supercritical regime where the order of the dissipation is small relative to order of the …

We establish the well/ill-posedness theories for the inviscid $\alpha $-surface quasi-
geostrophic ($\alpha $-SQG) equations in H\" older spaces, where $\alpha= 0$ and …

This paper considers a family of active scalar equations which modify the generalized
surface quasi-geostrophic (gSQG) equations through its constitutive law or dissipative …

This article studies the vortex-wave system for the Surface Quasi-Geostrophic equation with
parameter 0< s< 1. We obtained local existence of classical solutions in H^ 4 under the …

In this thesis we study the behaviour of several active scalar equations in spaces where
wellposedness is not expected, namely we study 2D-Euler, the Surface Quasi-Geostrophic …

The generalized surface quasi-geostrophic equations (gSQG) is a family of active scalar
transport equations that interpolates between the 2D incompressible Euler equation and the …