Titlebook: Convex Integration Applied to the Multi-Dimensional Compressible Euler Equations; Simon Markfelder Book 2021 The Editor(s) (if applicable)

倔强不能

Danielle Nierenberg,Katie Spodenompressible Euler systems (.), (.) and (.)–(.) are particular examples of hyperbolic conservation laws. In this chapter we deal with hyperbolic conservation laws in general. More details can be found in textbooks, e.g. by Dafermos [.].

ABASH

Simon MarkfelderProvides a genuinely compressible convex integration approach.Surveys most results achieved by convex integration.Explains the essentials of hyperbolic conservation laws

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Lecture Notes in Mathematicshttp://image.papertrans.cn/c/image/237843.jpg

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City Dynamics That Shape Vacant Land Use,In this book we deal with two examples of systems of conservation laws, namely the barotropic compressible Euler equations (.), (.) and the full compressible Euler equations (.)–(.), both of which are introduced in Chap. .. In this chapter we show that those two systems are indeed hyperbolic conservation laws as treated in Chap. ..

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Living reference work 2020Latest editionBefore we implement convex integration in the context of the barotropic Euler system in Chap. ., we prepare some ingredients needed for convex integration in this chapter. In Sect. . we adjust the problem in such a way that we can apply convex integration.

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Wolfgang Holnthoner,Andrea Banfi,Heinz RedlOur goal in this chapter is to prove the main result of this book, namely Theorem .. This theorem can be seen as a “compressible analogue” of a result by De Lellis and Székelyhidi, see [., Proposition 2] or [., Proposition 2.4].

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Botao Gao,Tatsuya Shimizu,Teruo OkanoIn this chapter we consider the initial boundary value problem for the barotropic Euler system (.), (.) with any given initial data (.) and impermeability boundary condition (.) on a bounded domain .. What is meant by an (admissible) weak solution to this problem is defined in Definition ..

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Aromatic

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The Euler Equations as a Hyperbolic System of Conservation LawsIn this book we deal with two examples of systems of conservation laws, namely the barotropic compressible Euler equations (.), (.) and the full compressible Euler equations (.)–(.), both of which are introduced in Chap. .. In this chapter we show that those two systems are indeed hyperbolic conservation laws as treated in Chap. ..