196 research outputs found
A mathematical clue to the separation phenomena on the two-dimensional Navier-Stokes equation
In general, before separating from a boundary, the flow moves toward reverse
direction near the boundary against the laminar flow direction. Here in this
paper, a clue to such reverse flow phenomena (in the mathematical sense) is
observed. More precisely, the non-stationary two-dimensional Navier-Stokes
equation with an initial datum having a parallel laminar flow (we define it
rigorously in the paper) is considered. We show that the direction of the
material differentiation is opposite to the initial flow direction and effect
of the material differentiation (inducing the reverse flow) becomes bigger when
the curvature of the boundary becomes bigger. We also show that the parallel
laminar flow cannot be a stationary Navier-Stokes flow near a portion of the
boundary with nonzero curvature
Long-time solvability of the Navier-Stokes-Boussinesq equations with almost periodic initial large data
We investigate large time existence of solutions of the
Navier-Stokes-Boussinesq equations with spatially almost periodic large data
when the density stratification is sufficiently large. In 1996, Kimura and
Herring \cite{KH} examined numerical simulations to show a stabilizing effect
due to the stratification. They observed scattered two-dimensional
pancake-shaped vortex patches lying almost in the horizontal plane. Our result
is a mathematical justification of the presence of such two-dimensional
pancakes. To show the existence of solutions for large times, we use
-norm of amplitudes. Existence for large times is then proven using
techniques of fast singular oscillating limits and bootstrapping argument from
a global-in-time unique solution of the system of limit equations
On dispersive effect of the Coriolis force for the stationary Navier-Stokes equations
The dispersive effect of the Coriolis force for the stationary Navier-Stokes
equations is investigated. The effect is of a different nature than the one
shown for the non-stationary case by J. Y. Chemin, B. Desjardins, I. Gallagher
and E. Grenier. Existence of a unique solution is shown for arbitrary large
external force provided the Coriolis force is large enough. The analysis is
carried out in a new framework of the Fourier-Besov spaces. In addition to the
stationary case counterparts of several classical results for the
non-stationary Navier-Stokes problem have been proven
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