Pulsating flows of the 2D Euler-Poisson equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:263

Article

Kwong, Man Kam¹  Yuen, Manwai² 

[1] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China

[2] Educ Univ Hong Kong, Dept Math & Informat Technol, 10 Lo Ping Rd, Hong Kong, Hong Kong, Peoples R China

关键词: Euler-Poisson equations;    Rotating fluids;    Pulsating;    Periodic solutions;    Pressureless fluids;   

DOI  :  10.1016/j.jde.2017.08.058

来源: Elsevier

【 摘 要 】

It is well known that solutions of gaseous or fluid dynamical systems can easily blowup or develop shock waves in finite time. In this paper we show the existence of a class of radially symmetric rotational solutions to the two-dimensional pressureless Euler-Poisson equations. The flows are global (i.e., exist for all t > 0), have compact support at all times, and pulsate periodically. The method of construction is novel. It comprises the piecing together of suitable shells of moving particles in a delicate manner with careful choice of initial data. Each shell is the solution of a member of a continuum of ordinary differential equations. Detailed analysis of the equations is carried out to ensure that neighboring shells can be chosen to pulsate with the same period. We also show that any such solution can be extended to a larger flow by adding annuli of pulsating flows. Our result exhibits another example of rotation preventing the blowup of solutions. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free