Existence theorems for the initial value problem of the cometary flow equation with an external force

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:405

Article

Zhang, Xianwen¹  Yin, Xiaoyang¹ 

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China

关键词: Cometary flow equation;    External force;    Lorentz field;    Cauchy problem;    Weak solution;   

DOI  :  10.1016/j.jmaa.2013.04.042

来源: Elsevier

【 摘 要 】

The initial value problem of the cometary flow equation with a given external force is investigated. By assuming that the initial microscopic density has finite mass and finite momentum and belongs to L-p for some p > 1, three existence results of weak solutions with mass conservation and local estimates for the kinetic energy are established for different external forces, each of which is assumed to be divergence free with respect to particle velocities. The first result deals with a bounded smooth force and a Lorentz force with bounded smooth electric and magnetic intensities, and the second one concerns a force belonging to L-q with 1/p + 1/q = 1. In the third theorem, we discuss a force that can be divided into two parts: one is in L-q and the other is linearly growing at infinity; in this case we need to assume further that the initial density has finite first order spatial moment. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free