The Existence and Uniqueness Theorem for Solution of Generalized Hydrodynamical Equation

TL;DR

This paper proves the existence and uniqueness of solutions for a generalized hydrodynamical equation using a new approach based on marginal observables and dual BBGKY hierarchy.

Contribution

It introduces a dual BBGKY hierarchy for microscopic observables and establishes a rigorous mathematical proof of solution existence and uniqueness.

Findings

Existence and uniqueness theorem for the generalized hydrodynamical equation.

Development of dual BBGKY hierarchy for microscopic observables.

Application of the theorem in the space of integrable functions.

Abstract

On the basis of the sequence of marginal observables the evolution equations of the microscopic phase density and its generalizations is discussed. We introduced dual BBGKY hierarchy for these microscopic observables and their average values. In the space of integrable functions, for initial-value problem of generalized hydrodynamical equation the existence and uniqueness theorem is proved.