三维圆柱体中非零涡度欧拉-泊松系统的超音速流动

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-07-22 DOI:10.1112/jlms.70233

Myoungjean Bae, Hyangdong Park

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引用次数: 0

摘要

证明了圆柱喷管中稳定欧拉-泊松系统三维超声速解的唯一存在性。首先，利用加权Sobolev范数建立了任意截面圆柱喷管无旋解的唯一存在性。然后，我们建立了非零涡度轴对称解在圆柱中的唯一存在性。讨论了非线性双曲-椭圆混合型偏微分方程（PDE）系统和Lipschitz域上的角点奇异性等问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Supersonic flows of the Euler–Poisson system with nonzero vorticities in three-dimensional cylinders

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Supersonic flows of the Euler–Poisson system with nonzero vorticities in three-dimensional cylinders

We prove the unique existence of three-dimensional supersonic solutions to the steady Euler–Poisson system in cylindrical nozzles. First, we establish the unique existence of irrotational solutions in a cylindrical nozzle with an arbitrary cross-section with using weighted Sobolev norms. Then, we establish the unique existence of axisymmetric solutions with nonzero vorticity in a circular cylinder. Several technical issues, including the issue of nonlinear hyperbolic–elliptic mixed type partial differential equation (PDE) system and corner singularities in a Lipschitz domain, are carefully addressed.

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.