Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-24T07:01:20.635Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-existence of global smooth solutions to symmetrizable nonlinear hyperbolic systems

Published online by Cambridge University Press:  12 July 2007

Tong Yang  and
Changjiang Zhu
Tong Yang
Affiliation:
Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong
Changjiang Zhu
Affiliation:
Laboratory of Nonlinear Analysis, Department of Mathematics, Central China Normal University, Wuhan 430079, People's Republic of China
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we consider the Cauchy problem of general symmetrizable hyperbolic systems in multi-dimensional space. When some components of the initial data have compact support, we give a sufficient condition on the non-existence of global C1 solutions. This non-existence theorem can be applied to some physical systems, such as Euler equations for compressible flow in multi-dimensional space. The blow-up phenomena here can come from the singularity developed at the interface, such as vacuum boundary, rather than the shock formation as studied in the previous works on strictly hyperbolic systems. Therefore, the systems considered here include those which are non-strictly hyperbolic.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 3 , June 2003 , pp. 719 - 728
Copyright
Copyright © Royal Society of Edinburgh 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)