期刊论文

Guo, Zhenhua

英文

IMA JOURNAL OF APPLIED MATHEMATICS

0272-4960

2006

71

5

658-669

10.1093/imamat/hxl013

This work partially comes from the first author’s Ph.D. thesis at The Institute of Mathematical Science, The Chinese University of Hong Kong. The first author expresses his deep gratitude to his graduate advisor, Prof. Zhouping Xin, for his guidance and encouragement. The authors would like to thank the referees for the useful remarks. ZG is supported in part by the National Natural Science Foundation of China (NSFC) (Grant No. 10401012) and by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, the State Education Ministry, while SJ by the (NSFC) (Grant No. 10225105), the National Basic Research Program (Grant No. 2005CB321700) and the China Academy of Engineering Physics (Grant No. 2003-R-02).

本校为第一且通讯机构

We investigate the self-similar solutions to the isothermal compressible Navier-Stokes equations. The aim of this paper is to show that there exist neither forward nor backward self-similar solutions with finite total energy. This generalizes the results for the incompressible case in Nečas, J., Ružička, M. & Šverák, V. (1996, On Leray's self-similar solutions of the Navier-Stokes equations. Acta. Math., 176, 283-294), and is consistent with the (unproved) existence of regular solutions globally in time for the compressib...