Which Measure-Valued Solutions of the Monoatomic Gas Equations are Generated by Weak Solutions?
Gallenmüller D, Wiedemann E (2023)
Publication Type: Journal article
Publication year: 2023
Journal
Book Volume: 247
Article Number: 61
Journal Issue: 4
DOI: 10.1007/s00205-023-01886-5
Abstract
Contrary to the incompressible case, not every measure-valued solution of the compressible Euler equations can be generated by weak solutions or a vanishing viscosity sequence. In the present paper we give sufficient conditions on an admissible measure-valued solution of the isentropic Euler system to be generated by weak solutions. As one of the crucial steps we prove a characterization result for generating A -free Young measures in terms of potential operators including uniform L∞ -bounds. More concrete versions of our results are presented in the case of a solution consisting of two Dirac measures. We conclude by discussing that are also necessary conditions for generating a measure-valued solution by weak solutions or a vanishing viscosity sequence and will point out that the resulting gap mainly results from obtaining only uniform Lp -bounds for 1 < p< ∞ instead of p= ∞ .
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Germany (DE)How to cite
APA:
Gallenmüller, D., & Wiedemann, E. (2023). Which Measure-Valued Solutions of the Monoatomic Gas Equations are Generated by Weak Solutions? Archive for Rational Mechanics and Analysis, 247(4). https://dx.doi.org/10.1007/s00205-023-01886-5
MLA:
Gallenmüller, Dennis, and Emil Wiedemann. "Which Measure-Valued Solutions of the Monoatomic Gas Equations are Generated by Weak Solutions?" Archive for Rational Mechanics and Analysis 247.4 (2023).
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