8,170 research outputs found
Global well-posedness for the Navier-Stokes-Boussinesq system with axisymmetric data
In this paper we prove the global well-posedness for a three-dimensional
Boussinesq system with axisymmetric initial data. This system couples the
Navier-Stokes equation with a transport-diffusion equation governing the
temperature. Our result holds uniformly with respect to the heat conductivity
coefficient which may vanish.Comment: 22 page
Global large solutions to 3-D inhomogeneous Navier-Stokes system with one slow variable
In this paper, we are concerned with the global wellposedness of 3-D
inhomogeneous incompressible Navier-Stokes equations \eqref{1.3} in the
critical Besov spaces with the norm of which are invariant by the scaling of
the equations and under a nonlinear smallness condition on the isentropic
critical Besov norm to the fluctuation of the initial density and the critical
anisotropic Besov norm of the horizontal components of the initial velocity
which have to be exponentially small compared with the critical anisotropic
Besov norm to the third component of the initial velocity. The novelty of this
results is that the isentropic space structure to the homogeneity of the
initial density function is consistent with the propagation of anisotropic
regularity for the velocity field. In the second part, we apply the same idea
to prove the global wellposedness of \eqref{1.3} with some large data which are
slowly varying in one direction
Optical data processing using paraboloidal mirror segments
An optical data processing system using paraboloidal reflecting surfaces is disclosed. In the preferred embodiment the paraboloidal reflecting surfaces are segments of a paraboloidal mirror. A source of coherent light is in the focal plane of the first paraboloidal mirror segment which collimates the beam and reflects it toward a second paraboloidal mirror surface. The information to be analyzed, on a transparency for example, is placed in the collimated beam. The beam is reflected from the second paraboloidal mirror segment and focused on a Fourier transform plane. A photon detector could be placed in the Fourier transform plane or suitable spatial filters, with the filtered beam then being reflected from a third paraboloidal mirror segment to be focused on a reconstruction plane
On the global well-posedness of the critical quasi-geostrophic equation
We prove the global well-posedness of the critical dissipative
quasi-geostrophic equation for large initial data belonging to the critical
Besov space $\dot B^0_{\infty,1}(\RR^2).
On the global existence for the axisymmetric Euler equations
This paper deals with the global well-posedness of the 3D axisymmetric Euler
equations for initial data lying in some critical Besov spacesComment: 14 page
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