Abstract
The pressure of a gas of particles with a uniformly repulsive pair interaction in a finite container is shown to satisfy (exactly as a formal object) a “viscous” Hamilton–Jacobi (H–J) equation whose solution in power series is recursively given by the variation of constants formula. We investigate the solution of the H–J and of its Legendre transform equation by the Cauchy-majorant method and provide a lower bound to the radius of convergence on the virial series of the fluid which goes beyond the threshold established by Lagrange’s inversion formula. Such results obtained in (On the virial series for a gas of particles with uniformly repulsive pairwise interactions (2014) Preprint) are reviewed and regarded as the first step towards the solution of a problem posed by Kac, Uhlenbeck and Hemmer (J. Math. Phys. 4 (1963) 216–228), questioning on the relation of the approach to the mean field theory with Ursell–Mayer expansion.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
