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- W3198990560 abstract "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 $${mathcal {A}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>A</mml:mi> </mml:math> -free Young measures in terms of potential operators including uniform $$L^{infty }$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>∞</mml:mi> </mml:msup> </mml:math> -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 $$L^p$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> </mml:math> -bounds for $$1<p<infty $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo><</mml:mo> <mml:mi>p</mml:mi> <mml:mo><</mml:mo> <mml:mi>∞</mml:mi> </mml:mrow> </mml:math> instead of $$p=infty $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>=</mml:mo> <mml:mi>∞</mml:mi> </mml:mrow> </mml:math> ." @default.
- W3198990560 created "2021-09-27" @default.
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- W3198990560 date "2023-06-05" @default.
- W3198990560 modified "2023-10-16" @default.
- W3198990560 title "Which Measure-Valued Solutions of the Monoatomic Gas Equations are Generated by Weak Solutions?" @default.
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