Abstract
In this paper we study one-dimensional viscous gas flows described by the Navier–Stokes equations. Thermodynamics of the gas obeys the van der Waals law. This implies that phase transitions can occur along the flow of such gas. The corresponding solutions are found as asymptotic expansions with respect to parameters a and b of the van der Waals equation. The zeroth and the first-order terms are obtained by means of symmetry methods and the corresponding space-time domains of phase transitions and different phases are shown.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Batchelor, G.K.: An introduction to fluid dynamics. Cambridge Univ. Press, Cambridge (2000).
Duyunova, A.A., Lychagin, V.V.,Tychkov, S.N.: Classification of equations of state for viscous fluids. Doklady Mathematics. 95, 172–175 (2017).
Duyunova, A.A., Lychagin, V.V.,Tychkov, S.N.: Differential invariants for flows of viscid fluids. J. Geom. Phys. 121, 309–316 (2017).
Vinogradov, A.M., Krasilshchik, I.S.: Symmetries and Conservation Laws for Differential Equations of Mathematical Physics. Factorial, Moscow (1997).
Krasilshchik, I.S., Lychagin, V.V., Vinogradov, A.M.: Geometry of Jet Spaces and Nonlinear Partial Differential Equations. Gordon and Breach Science Publishers (1986).
Lychagin, V.V.: Contact Geometry, Measurement and Thermodynamics. Lectures at Summer School, Wisla, 2018.
Acknowledgements
This work was supported by the Russian Foundation for Basic Research (project No 18-29-10013).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Gorinov, A.A., Lychagin, V.V., Roop, M.D., Tychkov, S.N. (2019). Gas Flow with Phase Transitions: Thermodynamics and the Navier–Stokes Equations. In: Kycia, R., Ułan, M., Schneider, E. (eds) Nonlinear PDEs, Their Geometry, and Applications. Tutorials, Schools, and Workshops in the Mathematical Sciences . Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-17031-8_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-17031-8_6
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-17030-1
Online ISBN: 978-3-030-17031-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)