Seminar talk, 25 February 2015: Difference between revisions
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| speaker = Valery Yumaguzhin | | speaker = Valery Yumaguzhin | ||
| title = Differential invariants on solutions of equations of adiabatic gas motion | | title = Differential invariants on solutions of equations of adiabatic gas motion | ||
| abstract = The talk will discuss the system of equations of adiabatic gas motion in <math alt=n>n</math>-dimensional space, <math alt=n=1,2,3>n=1,2,3</math> | | abstract = The talk will discuss the system of equations of adiabatic gas motion in <math alt='n'>n</math>-dimensional space, <math alt='n=1,2,3'>n=1,2,3</math>. | ||
Characteristic covectors of this system generate a geometric structure on every solution of this system. This structure consists of a hyperplane and a non degenerate cone in every cotangent space to a solution. These hyperplane and cone intersect in zero point only. | Characteristic covectors of this system generate a geometric structure on every solution of this system. This structure consists of a hyperplane and a non degenerate cone in every cotangent space to a solution. These hyperplane and cone intersect in zero point only. | ||
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In the case of polytropic gas motion, we calculate classes of explicit solutions possessing the linear connection with zero torsion. | In the case of polytropic gas motion, we calculate classes of explicit solutions possessing the linear connection with zero torsion. | ||
| slides = | | video = https://video.gdeq.org/GDEq-seminar-20150225-Valery_Yumaguzhin.mp4 | ||
| slides = [[Media:Yumaguzhin V. Differential invariants on solutions of equations of adiabatic gas motion (presentation at the Krasil'shchik's IUM Seminar, 25 February 2015).pdf|Yumaguzhin V. Differential invariants on solutions of equations of adiabatic gas motion (presentation at the Krasil'shchik's IUM Seminar, 25 February 2015).pdf]] | |||
| references = | | references = | ||
| 79YY-MM-DD = 7984-97-74 | | 79YY-MM-DD = 7984-97-74 | ||
}} | }} | ||
Latest revision as of 22:57, 30 March 2025
Speaker: Valery Yumaguzhin
Title: Differential invariants on solutions of equations of adiabatic gas motion
Abstract:
The talk will discuss the system of equations of adiabatic gas motion in -dimensional space, .
Characteristic covectors of this system generate a geometric structure on every solution of this system. This structure consists of a hyperplane and a non degenerate cone in every cotangent space to a solution. These hyperplane and cone intersect in zero point only.
We construct differential invariants of this structure: a vector field, a metric, and a linear connection with torsion in general position.
In the case of polytropic gas motion, we calculate classes of explicit solutions possessing the linear connection with zero torsion.
Video
Slides: Yumaguzhin V. Differential invariants on solutions of equations of adiabatic gas motion (presentation at the Krasil'shchik's IUM Seminar, 25 February 2015).pdf