Classes of smooth solutions to the multidimensional balance laws of gas dynamic type on the riemannian manifolds

TL;DR

This paper investigates special classes of solutions to multidimensional gas dynamic balance laws on Riemannian manifolds, focusing on solutions with separated variables and linear velocity profiles in Euclidean space.

Contribution

It introduces a new class of solutions with separated variables for multidimensional gas dynamic laws on Riemannian manifolds, expanding understanding of their structure.

Findings

Solutions with separated variables are characterized.

Linear velocity profile solutions are identified in Euclidean space.

The approach provides new insights into the structure of gas dynamic solutions.

Abstract

The paper is devoted to the special classes of solutions to multidimensional balance laws of gas dynamic type. In the velocity field for the solutions of such class the time and space variables are separated. The simplest case is the solution with the linear profile of velocity in the Euclidean space.