Global Ill‐Posedness of the Isentropic System of Gas Dynamics. Issue 7 (15th August 2014)

• Record Type: Journal Article
• Authors: Chiodaroli, Elisabetta; De Lellis, Camillo; Kreml, Ondřej
• Is Part Of: Communications on pure and applied mathematics. Volume 68:Issue 7(2015:Jul.)
• Page Start: 1157
• Page End: 1190
• Publication Date: 2014-08-15
• Subjects: Mathematics -- Periodicals; Mechanics -- Periodicals; Mathématiques -- Périodiques; Mécanique -- Périodiques; 510.5
• DOI: 10.1002/cpa.21537
• Languages: English
• ISSNs: 0010-3640

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>We consider the isentropic compressible Euler system in 2 space dimensions with pressure law <italic>p</italic> (<italic>ρ</italic>) = <italic>ρ</italic>² and we show the existence of classical Riemann data, i.e. pure jump discontinuities across a line, for which there are infinitely many admissible bounded weak solutions (bounded away from the void). We also show that some of these Riemann data are generated by a 1‐dimensional compression wave: our theorem leads therefore to Lipschitz initial data for which there are infinitely many global bounded admissible weak solutions. © 2015 Wiley Periodicals, Inc.</p> </abstract>