Long Time Behavior of Solutions to the 3D Compressible Euler Equations with Damping

Authors

Thomas C. Sideris, University of California, Santa Barbara
Becca Thomases, University of California, Santa BarbaraFollow
Dehua Wang, University of Pittsburgh

Document Type

Article

Publication Date

1-1-2003

Publication Title

Communications in Partial Differential Equations

Abstract

The effect of damping on the large-time behavior of solutions to the Cauchy problem for the three-dimensional compressible Euler equations is studied. It is proved that damping prevents the development of singularities in small amplitude classical solutions, using an equivalent reformulation of the Cauchy problem to obtain effective energy estimates. The full solution relaxes in the maximum norm to the constant background state at a rate of t-3/2. While the fluid vorticity decays to zero exponentially fast in time, the full solution does not decay exponentially. Formation of singularities is also exhibited for large data.

Keywords

Damping, Decay, Euler equations, Existence, Global smooth solutions, Singularities

Volume

28

Issue

3-4

First Page

795

Last Page

816

DOI

10.1081/PDE-120020497

ISSN

03605302

Comments

Peer reviewed accepted manuscript.

Recommended Citation

Sideris, Thomas C.; Thomases, Becca; and Wang, Dehua, "Long Time Behavior of Solutions to the 3D Compressible Euler Equations with Damping" (2003). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/174