131,808 research outputs found
Semiclassical analysis and sensitivity to initial conditions
We present several recent results concerning the transition between quantum
and classical mechanics, in the situation where the underlying dynamical system
has an hyperbolic behaviour. The special role of invariant manifolds will be
emphasized, and the long time evolution will show how the quantum
non-determinism and the classical chaotic sensitivity to initial conditions can
be compared, and in a certain sense overlap
Long-Time Asymptotics for the Navier-Stokes Equation in a Two-Dimensional Exterior Domain
We study the long-time behavior of infinite-energy solutions to the
incompressible Navier-Stokes equations in a two-dimensional exterior domain,
with no-slip boundary conditions. The initial data we consider are
finite-energy perturbations of a smooth vortex with small circulation at
infinity, but are otherwise arbitrarily large. Using a logarithmic energy
estimate and some interpolation arguments, we prove that the solution
approaches a self-similar Oseen vortex as . This result was
obtained in collaboration with Yasunori Maekawa (Kobe University).Comment: This is a non-technical presentation of the results obtained in
arXiv:1202.4969, including simplified proofs and additional information on
the convergence of vorticit
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