On the density of “wild” initial data for the compressible Euler system

Please always quote using this URN: urn:nbn:de:bvb:20-opus-232607
  • We consider a class of “wild” initial data to the compressible Euler system that give rise to infinitely many admissible weak solutions via the method of convex integration. We identify the closure of this class in the natural L1-topology and show that its complement is rather large, specifically it is an open dense set.

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Author: Eduard Feireisl, Christian Klingenberg, Simon Markfelder
Document Type:Journal article
Faculties:Fakultät für Mathematik und Informatik / Institut für Mathematik
Parent Title (English):Calculus of Variations and Partial Differential Equations
Year of Completion:2020
Article Number:152
Source:Calculus of Variations and Partial Differential Equations (2020) 59:152 https://doi.org/10.1007/s00526-020-01806-5
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Tag:Euler system
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Lxx Hyperbolic equations and systems [See also 58J45] / 35L65 Conservation laws
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q31 Euler equations [See also 76D05, 76D07, 76N10]
76-XX FLUID MECHANICS (For general continuum mechanics, see 74Axx, or other parts of 74-XX) / 76Nxx Compressible fluids and gas dynamics, general / 76N10 Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30]
Release Date:2021/05/25
Licence (German):License LogoCC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International