We consider the initial value problems of the incompressible Euler equations in the
rotational framework. We obtain the optimal range of the Strichartz estimate for the linear …

We study the well-posedness and ill-posedness for the Cauchy problem of the three-
dimensional primitive equations describing the large-scale oceanic and atmospheric …

We consider the initial value problem of the 3D incompressible Boussinesq equations for
rotating stratified fluids. We establish the dispersive and the Strichartz estimates for the …

In this paper, we consider the primitive equations with zero vertical viscosity, zero vertical
thermal diffusivity, and the horizontal viscosity and horizontal thermal diffusivity of size εα …

We establish the global well-posedness of the 3D fractional Boussinesq–Coriolis system
with stratification in a framework of Fourier type, namely spaces of Fourier–Besov type with …

Geophysical flows comprise a broad range of spatial and temporal scales, from planetary-to
meso-scale and microscopic turbulence regimes. The relation of scales and flow …

In a previous work we obtained a large lower bound for the lifespan of the solutions to the
Primitive Equations, and proved convergence to the 3D quasi-geostrophic system for …

This paper is devoted to the study of the lifespan of the solutions of the primitive equations
for less regular initial data. We interpolate the globall well-posedness results for small initial …

We study the lifespan and asymptotics (in the large rotation and stratification regime) for the
primitive system for highly ill-prepared initial data in critical spaces. Compared to our …

We consider the initial value problem of the 3D incompressible rotating Euler equations. We
prove the long time existence of classical solutions for initial data in Hs (R3) with s> 5/2 …