Abstract
The global behavior of the solutions to one-dimensional Navier-Stokes system with a free boundary is investigated for large data. It is shown that the solutions stabilize to equilibrium in general on subsequences, and completely, if the body force is such that the corresponding equilibrium is unique. Mild condition on state equation is imposed which is satisfied in important physical situations.
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
Preview
Unable to display preview. Download preview PDF.
References
Antoncev, S.N., Kaichov, A.V. and Monachov, V.N. (1993). Boundary value problems of mechanics of inhomogeneous fluids (Russian). Nauka, Novosibirsk.
Feireisl, E. and Petzeltová, H. (1997). On the long-time behaviour of solutions to the Navier-Stokes equations of compressible flow. Submitted to Arch. Rat. Mech. Anal.
Kuttler, K. (1990). InMal boundary value problems for the displacement in an isothermal, viscous gas. Nonlinear Anal., 15(7):601–623.
Matušů-Nečasová Š,: Okada, M. and Makino, T. (1997). Free boundary problem for the equation of spherically symmetric motion of viscous gas (III). Japan. J. Indust. Appl. Math., 14(2):199–213.
Nagasawa, T. (1989). On the one-dimensional free boundary problem for the heat conductive compressible viscous gas. Lecture Notes in Num. Appl. Anal., 10:83–99.
Novotný, A. and Straškraba, I. Convergence to equilibria for compressible Navier-Stokes equations with large data. Publications du Laboratoire ďAnalyse Non Linéaire Appliquée, Publication no. 98/03, UFR Science, Université de Toulon et du Var, BP 132, La Garde Cedex (France).
Straškraba I. (1996). Asymptotic development of vacuums for 1-D Navier-Stokes equations of compressible flow. To appear in Nonlinear World, 3:519–535.
Straškraba I. (1998). Large time behavior of solutions to compressible Navier-Stokes equations (Ed. R. Salvi). Pitman Res. Notes in Math. Series, 388:125–138.
Zlotnik, A.A., and Amosov, A.A. (1998). Generalized solutions in the large of equations of one-dimensional motion of a viscous barotropic gas (Russian). Doklady AN SSSR, 299(6):1303–1307.
Zlotnik, A. A. and Bao, N.Z. Properties and asymptotic behavior of solutions of a problem for one-dimensional motion of viscous barotropic gas (Russian). Mat. Zametki, 55(5):51–68.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Kluwer Academic Publishers
About this chapter
Cite this chapter
Penel, P., Straškraba, I. (2002). Global Behavior of Compressible Fluid with a Free Boundary and Large Data. In: Sequeira, A., da Veiga, H.B., Videman, J.H. (eds) Applied Nonlinear Analysis. Springer, Boston, MA. https://doi.org/10.1007/0-306-47096-9_29
Download citation
DOI: https://doi.org/10.1007/0-306-47096-9_29
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-306-46303-7
Online ISBN: 978-0-306-47096-7
eBook Packages: Springer Book Archive