國立虎尾科技大學 |

Convex Integration Applied to the Multi-Dimensional Compressible Euler Equations

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Convex Integration Applied to the Multi-Dimensional Compressible Euler Equations/ by Simon Markfelder.
Author:	Markfelder, Simon.
Description:	X, 242 p. 17 illus., 9 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Mathematical analysis. -
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. - 1st ed. 2021. - X, 242 p. 17 illus., 9 illus. in color.online resource. - Lecture Notes in Mathematics,22941617-9692 ;. - Lecture Notes in Mathematics,2144.

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 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:

527926
Mathematical analysis.

LC Class. No.: QA299.6-433

Dewey Class. No.: 515

Convex Integration Applied to the Multi-Dimensional Compressible Euler Equations
LDR:03014nam a22003975i 4500 001 1056430
003 DE-He213
005 20211020163829.0
007 cr nn 008mamaa
008 220103s2021 sz | s |||| 0|eng d
020 $a 9783030837853 $9 978-3-030-83785-3
024 7 $a 10.1007/978-3-030-83785-3 $2 doi
035 $a 978-3-030-83785-3
050 4 $a QA299.6-433
072 7 $a PBK $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBK $2 thema
082 0 4 $a 515 $2 23
100 1 $a Markfelder, Simon. $e author. $0 (orcid)0000-0002-0011-7597 $1 https://orcid.org/0000-0002-0011-7597 $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1361751
245 1 0 $a Convex Integration Applied to the Multi-Dimensional Compressible Euler Equations $h [electronic resource] / $c by Simon Markfelder.
250 $a 1st ed. 2021.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a X, 242 p. 17 illus., 9 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Lecture Notes in Mathematics, $x 1617-9692 ; $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 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 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 Mathematical analysis. $3 527926
650 0 $a Analysis (Mathematics). $3 1253570
650 0 $a Continuum physics. $3 1255031
650 0 $a Global analysis (Mathematics). $3 1255807
650 0 $a Manifolds (Mathematics). $3 1051266
650 1 4 $a Analysis. $3 669490
650 2 4 $a Classical and Continuum Physics. $3 1141497
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 672519
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030837846
776 0 8 $i Printed edition: $z 9783030837860
830 0 $a Lecture Notes in Mathematics, $x 0075-8434 ; $v 2144 $3 1254300
856 4 0 $u https://doi.org/10.1007/978-3-030-83785-3
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
912 $a ZDB-2-LNM
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)