Abstract
Compressible Euler equation is studied. First, we examine the validity of physical laws such as the conservations of total mass and energy and also the decay of total pressure. Then we show the non-existence of global-in-time irrotational solution with positive mass.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Acheson D.J.: Elementary Fluid Dynamics. Oxford University Press, New York (1990)
Feireisl E.: Dynamics of Viscous Compressible Fluids. Oxford University Press, Oxford (2004)
Kambe T.: Elementary Fluid Mechanics. World Scientific Publishing, Hackensack (2007)
Makino T., Ukai S., Kawashima S.: Sur la solution à à support compact de léquatioin d’Euler compressible. Jpn. J. Appl. Math. 3, 249–257 (1986)
Nishida T.: Global solution for an initial-boundary value problem of a quasilinear hyperbolic systems. Proc. Jpn. Acad. 44, 642–646 (1968)
Nishida T., Smoller J.: Solutions in the large for some nonlinear hyperbolic conservation laws. Commun. Pure Appl. Math. 26, 183–200 (1973)
Perthame B.: Kinetic Formulation of Conservation Laws. London, Oxford (2002)
Sideris T.C.: Formation of singularities in solutions to nonlinear hyperbolic equations. Arch. Ration. Mech. Anal. 86, 369–381 (1984)
Sideris T.C.: Formation of singularities in three-dimensional compressible fluids. Commun. Math. Phys. 101, 475–485 (1985)
Sideris T.C.: The lifespan of smooth solutions to the three-dimensional compressible Euler equations and the incompressible limit. Indiana Univ. Math. J. 40, 535–550 (1991)
Smoller J.: Shock Waves and Reaction-Diffusion Equations. Springer, Berlin (1982)
Xin Z.: Blowup of smooth solutions to the compressible Navier-Stokes equation with compact density. Commun. Pure Appl. Math. 51, 229–240 (1998)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by D. Chae
Rights and permissions
About this article
Cite this article
Suzuki, T. Irrotational Blowup of the Solution to Compressible Euler Equation. J. Math. Fluid Mech. 15, 617–633 (2013). https://doi.org/10.1007/s00021-012-0116-z
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00021-012-0116-z