Non-perturbative solution of the dual BBGKY hierarchy for hard-sphere fluids

Authors

DOI:

https://doi.org/10.15407/dopovidi2023.04.003

Keywords:

dual BBGKY hierarchy; cumulant; group of operators; hard-sphere fluids

Abstract

The communication presents a rigorous description of the evolution of observables of many colliding particles. For
expansions representing a solution of the Cauchy problem of the dual BBGKY hierarchy representations of their generating operators are established.

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References

Gerasimenko, V. I. & Gapyak, I. V. (2021). Boltzmann–Grad asymptotic behavior of collisional dynamics. Rev. in Math. Phys., 33, 2130001, 32. https://doi.org/10.1142/S0129055X21300016

Cercignani, C., Gerasimenko, V. & Petrina, D. (2012). Many-Particle Dynamics and Kinetic Equations. Second ed. Springer.

Gallagher, I., Saint-Raymond, L. & Texier, B. (2014). From Newton to Boltzmann: Hard Spheres and Shortrange Potentials. EMS Publ. House: Zürich Lectures in Adv. Math.

Gerasimenko, V. I. & Petrina, D. Ya. (1990). Mathematical problems of the statistical mechanics of a hardsphere system. Russ. Math. Surv. (Uspekhi Mat. Nauk) 45(3), pp. 135-182. https://doi.org/10.1070/RM1990v045n03ABEH002360

Gerasimenko, V. I. & Gapyak, I. V. (2022). Propagation of correlations in a hard-sphere system. J. Stat. Phys., 189, 2. https://doi.org/10.1007/s10955-022-02958-8

Pulvirenti, M. & Simonella, S. (2016). Propagation of chaos and effective equations in kinetic theory: a brief survey. Math. and Mech. of Complex Systems, 4, No. 3-4, pp. 255-274. https://doi.org/10.2140/memocs.2016.4.255

Gallagher, I. (2019). From Newton to Navier–Stokes, or how to connect fluid mechanics equations from microscopic to macroscopic scales. Bull. Amer. Math. Soc. 56, No. 1, pp. 65-85. https://doi.org/10.1090/bull/1650

Gerasimenko, V. I. & Gapyak, I. V. (2018). Low-density asymptotic behavior of observables of hard sphere fluids. Advances in Math. Phys., 2018. Article ID 6252919. https://doi.org/10.1155/2018/6252919

Borgioli, G. & Gerasimenko, V. I. (2001). The dual BBGKY hierarchy for the evolution of observables. Riv. Mat. Univ. Parma, 4, pp. 251-267.

Gerasimenko, V. I. & Ryabukha, T. V. (2002). Cumulant representation of solutions of the BBGKY hierarchy of equations. Ukrainian Math. J., 54(10), pp. 1583-1601. https://doi.org/10.1023/A:1023771917748

Gerasimenko, V. I. & Ryabukha, T. V. (2003). On the dual nonequilibrium cluster expansion. Dopov. Nac. akad. nauk Ukr., No. 3, pp. 16-22.

Gerasimenko, V. I., Ryabukha, T. V. & Stashenko, M. O. (2004). On the structure of expansions for the BBGKY hierarchy solutions, J. Phys. A: Math. Gen., 37, pp. 9861-9872. https://doi.org/10.1088/0305-4470/37/42/002

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Published

08.09.2023

How to Cite

Gerasimenko, V., & Gapyak, I. (2023). Non-perturbative solution of the dual BBGKY hierarchy for hard-sphere fluids. Reports of the National Academy of Sciences of Ukraine, (4), 3–10. https://doi.org/10.15407/dopovidi2023.04.003

Section

Mathematics