Singularity formation for one dimensional full Euler equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:261

Article

Pan, Ronghua¹  Zhu, Yi² 

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

关键词: Compressible Euler equations;    Singularity formation;    Global regularity;    Large data;   

DOI  :  10.1016/j.jde.2016.09.015

来源: Elsevier

【 摘 要 】

We investigate the basic open question on the global existence v.s. finite time blow-up phenomena of classical solutions for the one-dimensional compressible Euler equations of adiabatic flow. For isentropic flows, it is well-known that the solutions develop singularity if and only if initial data contain any compression (the Rieman variables have negative spatial derivative). The situation for non-isentropic flow is not quite clear so far, due to the presence of non-constant entropy. In [4], it is shown that initial weak compressions do not necessarily develop singularity in finite time, unless the compression is strong enough for general data. In this paper, we identify a class of solutions of the full (non-isentropic) Euler equations, developing singularity in finite time even though their initial data do not contain any compression. This is in sharp contrast to the isentropic flow. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free