23 research outputs found
Self-similar asymptotics of solutions to the Navier-Stokes system in two dimensional exterior domain
We consider the 2D incompressible Navier-Stokes equations with Dirichlet
boundary condition in the exterior of one obstacle. Assuming that the
circulation at infinity of the velocity is sufficiently small, we prove that
the large time behavior of the corresponding solution to the initial-boundary
value problem is described by the Lamb-Oseen vortex. The later is the
well-known explicit self-similar solution to the Navier-Stokes system in the
whole space .Comment: 13 page
Stabilité et asymptotique en temps grand de solutions globales des équations de Navier-Stokes
Non-explosion en temps grand et stabilité de solutions globales des équations de Navier–Stokes
Mathematical justification of the hydrostatic approximation in the primitive equations of geophysical fluid dynamics
Geophysical fluids all exhibit a common feature: their aspect ratio (depth to horizontal width) is very small. This leads to an asymptotic model widely used in meteorology, oceanography, and limnology, namely the hydrostatic approximation of the time-dependent incompressible Navier–Stokes equations. It relies on the hypothesis that pressure increases linearly in the vertical direction. In the following, we prove a convergence and existence theorem for this model by means of anisotropic estimates and a new time-compactness criterium.Fonds Franco-Espagnol D.R.E.I.FMinisterio de Educación y Cienci
Asymptotics of solutions to the Navier-Stokes system in exterior domains
We consider the incompressible Navier-Stokes equations with the Dirichlet
boundary condition in an exterior domain of with . We
compare the long-time behaviour of solutions to this initial-boundary value
problem with the long-time behaviour of solutions of the analogous Cauchy
problem in the whole space . We find that the long-time
asymptotics of solutions to both problems coincide either in the case of small
initial data in the weak -space or for a certain class of large initial
data
The FENE dumbbell polymer model: existence and uniqueness of solutions for the momentum balance equation
We consider the FENE dumbbell polymer model which is the coupling of the
incompressible Navier-Stokes equations with the corresponding
Fokker-Planck-Smoluchowski di ffusion equation. We show global well-posedness
in the case of a 2D bounded domain. We assume in the general case that the
initial velocity is sufficiently small and the initial probability density is
sufficiently close to the equilibrium solution; moreover an additional
condition on the coeffcients is imposed. In the corotational case, we only
assume that the initial probability density is sufficiently close to the
equilibrium solution