TY - JOUR

T1 - Formation of Unstable Shocks for 2D Isentropic Compressible Euler

AU - Buckmaster, Tristan

AU - Iyer, Sameer

N1 - Funding Information:
Tristan Buckmaster partially supported by NSF Grant DMS-1900149 and a Simons Foundation Mathematical and Physical Sciences Collaborative Grant. Sameer Iyer partially supported by NSF Grant DMS-1802940.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2021

Y1 - 2021

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

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

ER -