可压缩流体流动欧拉方程熵解的全局存在性

IF 1.3 2区数学 Q1 MATHEMATICS

Mathematische Annalen Pub Date : 2024-06-18 DOI:10.1007/s00208-024-02922-9

Yun-guang Lu, Christian Klingenberg, Xiangxing Tao

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引用次数: 0

摘要

本文的主要贡献是完整地证明了一维可压缩流体流动欧拉方程 Cauchy 问题的全局弱熵解存在性，并纠正了 "半导体一维流体力学模型的全局弱解"（Math.Mod.Meth.应用科学》，6（1993），759-788）中的错误。我们的技术是人工粘度法与补偿紧凑性理论相结合的方法，其中通过经典的富强方程构建了四个拉克斯熵通量对系列。

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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Global existence of entropy solutions for euler equations of compressible fluid flow

The main contribution of this paper is to provide a complete proof of the global weak entropy solution existence of the Cauchy problem for the Euler equations of one-dimensional compressible fluid flow and to correct the mistakes in the paper “Global weak solutions of the one-dimensional hydrodynamic model for semiconductors” (Math. Mod. Meth. Appl. Sci., 6(1993), 759–788). Our technique is the method of the artificial viscosity coupled with the theory of compensated compactness, where four families of Lax entropy-entropy flux pair are constructed by means of the classical Fuchsian equation.

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来源期刊

Mathematische Annalen 数学-数学

CiteScore

2.90

自引率

7.10%

发文量

181

审稿时长

4-8 weeks

期刊介绍： Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin. The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin. Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.