Blowup for the compressible isothermal Euler equations with non-vacuum initial data

ABSTRACT

In this paper, we study the compressible isothermal Euler equations with non-vacuum initial data. First, we prove the property of finite propagation to this Cauchy problem by using local energy estimates. Second, we establish the blowup results of the multi-dimensional case in radial symmetry and the one-dimensional case in non-radial symmetry by making assumptions on the initial velocity. Third, we present the blowup results of the three-dimensional case in non-radial symmetry by making assumptions on the initial momentum.

COMMUNICATED BY:

• Francisco Sayas

KEYWORDS:

• Isothermal Euler equations
• Cauchy problem
• finite propagation
• blowup

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35B44
• 35L67
• 35Q31
• 35B30

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors acknowledge support from the Natural Science Foundation of Henan Province Science and Technology Department [grant number 162300410077], the Aeronautical Science Foundation of China Youth Natural Science Foundation of Zhengzhou University of Aeronautics [grant number 2015113001], the Project of Youth Backbone Teachers of Colleges and Universities in Henan Province [grant number 2013GGJS-142] and National Natural Science Foundation of China (NSFC) [grant number 11501525], Aeronautical Science Foundation of China [grant number 2017ZD55014], and Outstanding Youth Foundation of Science & Technology Innovation of Henan Province [grant number 2018JQ0004].