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

In this paper, exact solutions with a linear velocity field are sought for the gas dynamics equations in the case of the special state equation and the state equation of a monatomic gas. These state equations extend the transformation group admitted by the system to 12 and 14 parameters, respectively. Invariant submodels of rank one are constructed from two three-dimensional subalgebras of the corresponding Lie algebras, and exact solutions with a linear velocity field with inhomogeneous deformation are obtained. On the one hand of the special state equation, the submodel describes an isochoric vortex motion of particles, isobaric along each world line and restricted by a moving plane. The motions of particles occur along parabolas and along rays in parallel planes. The spherical volume of particles turns into an ellipsoid at finite moments of time, and as time tends to infinity, the particles end up on an infinite strip of finite width. On the other hand of the state equation of a monatomic gas, the submodel describes vortex compaction to the origin and the subsequent expansion of gas particles in half-spaces. The motion of any allocated volume of gas retains a spherical shape. It is shown that for any positive moment of time, it is possible to choose the radius of a spherical volume such that the characteristic conoid beginning from its center never reaches particles outside this volume. As a result of the generalization of the solutions with a linear velocity field, exact solutions of a wider class are obtained without conditions of invariance of density and pressure with respect to the selected three-dimensional subalgebras.

New Exact Solutions with a Linear Velocity Field for the Gas Dynamics Equations for Two Types of State Equations