國立高雄大學圖資館 |

Language: English

Back

Convex integration applied to the mu...

Markfelder, Simon.

Convex integration applied to the multi-dimensional compressible Euler equations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Convex integration applied to the multi-dimensional compressible Euler equationsby Simon Markfelder.
Author:	Markfelder, Simon.
Published:	Cham :Springer International Publishing :2021.
Description:	x, 242 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Lagrange equations.
Online resource:	https://doi.org/10.1007/978-3-030-83785-3
ISBN:	9783030837853$q(electronic bk.)

Convex integration applied to the multi-dimensional compressible Euler equations
Markfelder, Simon.

Convex integration applied to the multi-dimensional compressible Euler equations[electronic resource] /by Simon Markfelder. - Cham :Springer International Publishing :2021. - x, 242 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 22941617-9692 ;. - Lecture notes in mathematics ;2035..

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 Szekelyhidi 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-Szekelyhidi 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 boundary value problem for the Euler system. Next some applications of this theorem are discussed, in particular concerning the Riemann problem. Finally there is a survey of some related results. This self-contained book is suitable for both beginners in the field of hyperbolic conservation laws as well as for advanced readers who already know about convex integration in the incompressible framework.

ISBN: 9783030837853$q(electronic bk.)

Standard No.: 10.1007/978-3-030-83785-3doiSubjects--Topical Terms:

226585
Lagrange equations.

LC Class. No.: QA614.8 / .M37 2021

Dewey Class. No.: 515.35

Convex integration applied to the multi-dimensional compressible Euler equations
LDR:02657nmm a2200325 a 4500 001 610771
003 DE-He213
005 20211020163829.0
006 m d
007 cr nn 008maaau
008 220330s2021 sz s 0 eng d
020 $a 9783030837853$q(electronic bk.)
020 $a 9783030837846$q(paper)
024 7 $a 10.1007/978-3-030-83785-3 $2 doi
035 $a 978-3-030-83785-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA614.8 $b .M37 2021
072 7 $a PBK $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBK $2 thema
082 0 4 $a 515.35 $2 23
090 $a QA614.8 $b .M345 2021
100 1 $a Markfelder, Simon. $3 908959
245 1 0 $a Convex integration applied to the multi-dimensional compressible Euler equations $h [electronic resource] / $c by Simon Markfelder.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a x, 242 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 1617-9692 ; $v v. 2294
520 $a 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 Szekelyhidi 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-Szekelyhidi 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 boundary value problem for the Euler system. Next some applications of this theorem are discussed, in particular concerning the Riemann problem. Finally there is a survey of some related results. This self-contained book is suitable for both beginners in the field of hyperbolic conservation laws as well as for advanced readers who already know about convex integration in the incompressible framework.
650 0 $a Lagrange equations. $3 226585
650 0 $a Convex functions. $3 191128
650 0 $a Numerical integration. $3 229132
650 0 $a Boundary value problems. $3 206979
650 1 4 $a Analysis. $3 273775
650 2 4 $a Classical and Continuum Physics. $3 771188
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 273786
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Lecture notes in mathematics ; $v 2035. $3 557764
856 4 0 $u https://doi.org/10.1007/978-3-030-83785-3
950 $a Mathematics and Statistics (SpringerNature-11649)