東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Convex integration applied to the mu...

Markfelder, Simon.

Linked to FindBook

Google Book

Amazon

博客來

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 equations/ by 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

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 ;v. 2294..

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

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

888591
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 2253797
003 DE-He213
005 20211020163829.0
006 m d
007 cr nn 008maaau
008 220327s2021 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 3522350
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 888591
650 0 $a Convex functions. $3 544201
650 0 $a Numerical integration. $3 596300
650 0 $a Boundary value problems. $3 527599
650 1 4 $a Analysis. $3 891106
650 2 4 $a Classical and Continuum Physics. $3 3218450
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 891107
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Lecture notes in mathematics ; $v v. 2294. $3 3522351
856 4 0 $u https://doi.org/10.1007/978-3-030-83785-3
950 $a Mathematics and Statistics (SpringerNature-11649)