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Studiamo l'evoluzione temporale di un fluido bidimensionale incomprimibile non viscoso quando la vorticità iniziale è concentrata in regioni di diametro e mostriamo che la vorticità evoluta temporalmente è anche lei concentrata in piccole regioni di diametro , per qualunque . Noi chiamiamo questa proprietà "localizzazione". Come conseguenza abbiamo una connessione rigorosa tra il modello dei vortici puntiformi e l'Equazione di Eulero.
Si considera un sistema bidimensionale di particelle interagenti tramite un potenziale di Newton o di Coulomb e si mostra che l’insieme delle condizioni iniziali che in un tempo finito possono condurre a delle singolarità possiede misura di Lebesgue nulla.
Si considera un sistema bidimensionale di particelle interagenti tramite un potenziale di Newton o di Coulomb e si mostra che l’insieme delle condizioni iniziali che in un tempo finito possono condurre a delle singolarità possiede misura di Lebesgue nulla.
We consider a body immersed in a perfect gas and moving under the action of a constant force.
Body and gas are in thermal equilibrium. We assume a stochastic interaction body/medium: when a particle of the medium hits the body,
it is absorbed and immediately re-emitted with a Maxwellian distribution. This system gives rise to a microscopic model of friction.
We study the approach of the body velocity to the limiting velocity and prove that, under suitable smallness
assumptions, the approach...
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