English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We analyze the stability of stationary solutions of a singular Vlasov typehydrodynamic equation (HE). This equation was derived (under suitableassumptions) as the hydrodynamical scaling limit of the Hamiltonian evolutionof a system consisting of a massive piston immersed in an ideal gas of pointparticles in a box. We find explicit criteria for global stability as well as aclass of solutions which are linearly unstable for a dense set of parametervalues. We present evidence (but no proof) that when the mechanical system hasinitial conditions ``close'' to stationary stable solutions of the HE then itstays close to these solutions for a time which is long compared to that forwhich the equations have been derived. On the other hand if the initial stateof the particle system is close to an unstable stationary solutions of the HEthe mechanical motion follows for an extended time a perturbed solution of thatequation: we find such approximate periodic solutions that are linearly stable.Comment: 31 pages, 7 figure

Stability of solutions of hydrodynamic equations describing the scaling limit of a massive piston in an ideal gas