7 research outputs found
On the global well-posedness for the Boussinesq system with horizontal dissipation
In this paper, we investigate the Cauchy problem for the tridimensional
Boussinesq equations with horizontal dissipation. Under the assumption that the
initial data is an axisymmetric without swirl, we prove the global
well-posedness for this system. In the absence of vertical dissipation, there
is no smoothing effect on the vertical derivatives. To make up this
shortcoming, we first establish a magic relationship between
and by taking full advantage of the structure of the
axisymmetric fluid without swirl and some tricks in harmonic analysis. This
together with the structure of the coupling of \eqref{eq1.1} entails the
desired regularity.Comment: 32page
On the Uniqueness of Solutions to Boundary Value Problems for Non-stationary Euler Equations
Some criteria concerning the vorticity and the problem of global regularity for the 3D Navier-Stokes equations
We review some results concerning the problem of global-in-time regularity for the initial boundary value problem for the Navier-Stokes equations in three-dimensional domains. In particular, we focus on sufficient conditions on the vorticity field which imply that strong (hence smooth) solutions exist on arbitrary time intervals