TY - JOUR
T1 - Variation Instability Near Vacuum in One-Dimensional Isentropic Flow
AU - Jenssen, Helge Kristian
N1 - Publisher Copyright:
© 2022 The Author(s). Published by Oxford University Press. All rights reserved.
PY - 2023/8/1
Y1 - 2023/8/1
N2 - 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$]]>, whereas no such instability occurs for.
AB - We consider instability of the total variation in shock-only solutions to the one-dimensional isentropic Euler system. The main results concern the possibility of immediate blowup in variation of the density field when the data approaches vacuum. In the case of an initially bounded velocity field, it is verified that immediate variation blowup in can occur whenever the adiabatic exponent satisfies 3$]]>, whereas no such instability occurs for.
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U2 - 10.1093/imrn/rnac251
DO - 10.1093/imrn/rnac251
M3 - Article
AN - SCOPUS:85172457462
SN - 1073-7928
VL - 2023
SP - 14929
EP - 14954
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 17
ER -