Variation Instability Near Vacuum in One-Dimensional Isentropic Flow

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We consider instability of the total variation in shock-only solutions to the one-dimensional isentropic Euler system. The main results concern the possibility of immediate blowup in variation of the density field when the data approaches vacuum. In the case of an initially bounded velocity field, it is verified that immediate variation blowup in can occur whenever the adiabatic exponent satisfies 3$]]>, whereas no such instability occurs for.

Original languageEnglish (US)
Pages (from-to)14929-14954
Number of pages26
JournalInternational Mathematics Research Notices
Issue number17
StatePublished - Aug 1 2023

All Science Journal Classification (ASJC) codes

  • General Mathematics

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