| 书目名称 | Convex Integration Applied to the Multi-Dimensional Compressible Euler Equations |
| 编辑 | Simon Markfelder |
| 视频video | |
| 概述 | Provides a genuinely compressible convex integration approach.Surveys most results achieved by convex integration.Explains the essentials of hyperbolic conservation laws |
| 丛书名称 | Lecture Notes in Mathematics |
| 图书封面 |  |
| 描述 | This book applies the convex integration method to multi-dimensional compressible Euler equations in the barotropic case as well as the full system with temperature. The convex integration technique, originally developed in the context of differential inclusions, was applied in the groundbreaking work of De Lellis and Székelyhidi to the incompressible Euler equations, leading to infinitely many solutions. This theory was later refined to prove non-uniqueness of solutions of the compressible Euler system, too. These non-uniqueness results all use an ansatz which reduces the equations to a kind of incompressible system to which a slight modification of the incompressible theory can be applied. This book presents, for the first time, a generalization of the De Lellis–Székelyhidi approach to the setting of compressible Euler equations..The structure of this book is as follows: after providing an accessible introduction to the subject, including the essentials of hyperbolic conservation laws, the idea of convex integration in the compressible framework is developed. The main result proves that under a certain assumption there exist infinitely many solutions to an abstract initial bounda |
| 出版日期 | Book 2021 |
| 关键词 | Admissible Weak Solutions; Barotropic Euler Equations; Barotropic Euler System; Compressible Euler Equa |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-030-83785-3 |
| isbn_softcover | 978-3-030-83784-6 |
| isbn_ebook | 978-3-030-83785-3Series ISSN 0075-8434 Series E-ISSN 1617-9692 |
| issn_series | 0075-8434 |
| copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
发表于 2025-3-21 16:42:55
