835 research outputs found
Speedy motions of a body immersed in an infinitely extended medium
We study the motion of a classical point body of mass M, moving under the
action of a constant force of intensity E and immersed in a Vlasov fluid of
free particles, interacting with the body via a bounded short range potential
Psi. We prove that if its initial velocity is large enough then the body
escapes to infinity increasing its speed without any bound "runaway effect".
Moreover, the body asymptotically reaches a uniformly accelerated motion with
acceleration E/M. We then discuss at a heuristic level the case in which Psi(r)
diverges at short distances like g r^{-a}, g,a>0, by showing that the runaway
effect still occurs if a<2.Comment: 15 page
2-D constrained Navier-Stokes equation and intermediate asymptotics
We introduce a modified version of the two-dimensional Navier-Stokes
equation, preserving energy and momentum of inertia, which is motivated by the
occurrence of different dissipation time scales and related to the gradient
flow structure of the 2-D Navier-Stokes equation. The hope is to understand
intermediate asymptotics. The analysis we present here is purely formal. A
rigorous study of this equation will be done in a forthcoming paper
On the propagation of a perturbation in an anharmonic system
We give a not trivial upper bound on the velocity of disturbances in an
infinitely extended anharmonic system at thermal equilibrium. The proof is
achieved by combining a control on the non equilibrium dynamics with an
explicit use of the state invariance with respect to the time evolution.Comment: 14 page
The Vortex-Wave equation with a single vortex as the limit of the Euler equation
In this article we consider the physical justification of the Vortex-Wave
equation introduced by Marchioro and Pulvirenti in the case of a single point
vortex moving in an ambient vorticity. We consider a sequence of solutions for
the Euler equation in the plane corresponding to initial data consisting of an
ambient vorticity in and a sequence of concentrated blobs
which approach the Dirac distribution. We introduce a notion of a weak solution
of the Vortex-Wave equation in terms of velocity (or primitive variables) and
then show, for a subsequence of the blobs, the solutions of the Euler equation
converge in velocity to a weak solution of the Vortex-Wave equation.Comment: 24 pages, to appea
CuckerâSmale Type Dynamics of Infinitely Many Individuals with Repulsive Forces
We study the existence and uniqueness of the time evolution of a system of infinitely many individuals, moving in a tunnel and subjected to a CuckerâSmale type alignment dynamics with compactly supported communication kernels and to short-range repulsive interactions to avoid collisions
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