TY - JOUR
T1 - Formation of Unstable Shocks for 2D Isentropic Compressible Euler
AU - Buckmaster, Tristan
AU - Iyer, Sameer
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2022/1
Y1 - 2022/1
N2 - In this paper we construct unstable shocks in the context of 2D isentropic compressible Euler in azimuthal symmetry. More specifically, we construct initial data that when viewed in self-similar coordinates, converges asymptotically to the unstable C15 self-similar solution to the Burgers’ equation. Moreover, we show the behavior is stable in C8 modulo a two dimensional linear subspace. Under the azimuthal symmetry assumption, one cannot impose additional symmetry assumptions in order to isolate the corresponding manifold of initial data leading to stability: rather, we rely on modulation variable techniques in conjunction with a Newton scheme.
AB - In this paper we construct unstable shocks in the context of 2D isentropic compressible Euler in azimuthal symmetry. More specifically, we construct initial data that when viewed in self-similar coordinates, converges asymptotically to the unstable C15 self-similar solution to the Burgers’ equation. Moreover, we show the behavior is stable in C8 modulo a two dimensional linear subspace. Under the azimuthal symmetry assumption, one cannot impose additional symmetry assumptions in order to isolate the corresponding manifold of initial data leading to stability: rather, we rely on modulation variable techniques in conjunction with a Newton scheme.
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U2 - 10.1007/s00220-021-04271-z
DO - 10.1007/s00220-021-04271-z
M3 - Article
AN - SCOPUS:85120349663
SN - 0010-3616
VL - 389
SP - 197
EP - 271
JO - Communications In Mathematical Physics
JF - Communications In Mathematical Physics
IS - 1
ER -