Smooth Subsonic and Transonic Spiral Flows with Nonzero Vorticity to Steady Euler–Poisson System in Concentric Cylinders

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Nonlinear Science Pub Date : 2024-06-24 DOI:10.1007/s00332-024-10057-z

Shangkun Weng, Wengang Yang, Na Zhang

引用次数: 0

Abstract

Both smooth subsonic and transonic spiral flows to steady Euler–Poisson system with nonzero angular velocity and vorticity in a concentric cylinder are studied. On the one hand, we investigate the structural stability of smooth cylindrically symmetric subsonic flows under three-dimensional perturbations on the inner and outer cylinders. On the other hand, the structural stability of smooth transonic flows under the axi-symmetric perturbations is examined. There are no any restrictions on the background subsonic and transonic solutions. A deformation-curl-Poisson decomposition to the steady Euler–Poisson system is utilized to deal with the hyperbolic-elliptic mixed structure in the subsonic region. We emphasize that there is a special structure of the steady Euler–Poisson system which yields a priori estimates and uniqueness of the linearized elliptic system.

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同心圆柱体中具有非零涡度的平稳亚音速和跨音速螺旋流动与稳定欧拉-泊松系统

我们研究了同心圆柱体中具有非零角速度和涡度的稳定欧拉-泊松系统的平稳亚音速和跨音速螺旋流。一方面，我们研究了光滑圆柱对称亚音速流在内外圆柱三维扰动下的结构稳定性。另一方面，我们研究了平滑跨音速流在轴对称扰动下的结构稳定性。背景亚音速和跨音速解不受任何限制。利用对稳定欧拉-泊松系统的变形-卷曲-泊松分解来处理亚音速区域的双曲-椭圆混合结构。我们强调，稳定欧拉-泊松系统有一种特殊结构，可产生线性化椭圆系统的先验估计和唯一性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Nonlinear Science 数学-力学

CiteScore

5.00

自引率

3.30%

发文量

审稿时长

4.5 months

期刊介绍： The mission of the Journal of Nonlinear Science is to publish papers that augment the fundamental ways we describe, model, and predict nonlinear phenomena. Papers should make an original contribution to at least one technical area and should in addition illuminate issues beyond that area''s boundaries. Even excellent papers in a narrow field of interest are not appropriate for the journal. Papers can be oriented toward theory, experimentation, algorithms, numerical simulations, or applications as long as the work is creative and sound. Excessively theoretical work in which the application to natural phenomena is not apparent (at least through similar techniques) or in which the development of fundamental methodologies is not present is probably not appropriate. In turn, papers oriented toward experimentation, numerical simulations, or applications must not simply report results without an indication of what a theoretical explanation might be. All papers should be submitted in English and must meet common standards of usage and grammar. In addition, because ours is a multidisciplinary subject, at minimum the introduction to the paper should be readable to a broad range of scientists and not only to specialists in the subject area. The scientific importance of the paper and its conclusions should be made clear in the introduction-this means that not only should the problem you study be presented, but its historical background, its relevance to science and technology, the specific phenomena it can be used to describe or investigate, and the outstanding open issues related to it should be explained. Failure to achieve this could disqualify the paper.