TY - JOUR

T1 - On Self-similar Solutions to Degenerate Compressible Navier–Stokes Equations

AU - Germain, Pierre

AU - Iwabuchi, Tsukasa

AU - Léger, Tristan

N1 - Funding Information:
P. Germain was partially supported by the NSF Grant DMS-1501019. T. Iwabuchi was supported by JSPS KAKENHI Grant 17H04824.
Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2021/2

Y1 - 2021/2

N2 - We study cavitating solutions to compressible Navier–Stokes equations with degenerate density-dependent viscosity. We consider two types of small radial solutions: forward self-similar (expanders), and backward self-similar (shrinkers). In the first case, we construct such solutions by a fixed-point argument. In the second case, we prove non-existence of such solutions using weighted energy estimates.

AB - We study cavitating solutions to compressible Navier–Stokes equations with degenerate density-dependent viscosity. We consider two types of small radial solutions: forward self-similar (expanders), and backward self-similar (shrinkers). In the first case, we construct such solutions by a fixed-point argument. In the second case, we prove non-existence of such solutions using weighted energy estimates.

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U2 - 10.1007/s00220-020-03919-6

DO - 10.1007/s00220-020-03919-6

M3 - Article

AN - SCOPUS:85096390161

VL - 381

SP - 1001

EP - 1030

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -