Two-dimensional vortex sheets for the nonisentropic Euler equations: Nonlinear stability

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Morando, Alessandro¹  Trebeschi, Paola¹  Wang, Tao^2,3 

[1] Univ Brescia, DICATAM, Via Valotti 9, I-25133 Brescia, Italy

[2] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China

[3] Wuhan Univ, Hubei Key Lab Computat Sci, Wuhan 430072, Hubei, Peoples R China

关键词: Nonisentropic fluid;    Compressible vortex sheet;    Characteristic boundary;    Existence;    Nonlinear stability;    Nash-Moser iteration;   

DOI  :  10.1016/j.jde.2018.10.029

来源: Elsevier

【 摘 要 】

We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando and Trebeschi (2008) [20]. The missing normal derivatives are compensated through the equations of the linearized vorticity and entropy when deriving higher-order energy estimates. The proof of the resolution for this nonlinear problem follows from certain a priori tame estimates on the effective linear problem in the usual Sobolev spaces and a suitable Nash-Moser iteration scheme. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free