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

Pierre Germain; Tsukasa Iwabuchi; Tristan Léger

doi:10.1007/s00220-020-03919-6

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

Pierre Germain, Tsukasa Iwabuchi, Tristan Léger

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Pages (from-to)	1001-1030
Number of pages	30
Journal	Communications In Mathematical Physics
Volume	381
Issue number	3
DOIs	https://doi.org/10.1007/s00220-020-03919-6
State	Published - Feb 2021

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1007/s00220-020-03919-6

Cite this

@article{9500dd25e8a2457eb3614e5f7b135570,

title = "On Self-similar Solutions to Degenerate Compressible Navier–Stokes Equations",

abstract = "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.",

author = "Pierre Germain and Tsukasa Iwabuchi and Tristan L{\'e}ger",

note = "Publisher Copyright: {\textcopyright} 2020, Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2021",

month = feb,

doi = "10.1007/s00220-020-03919-6",

language = "English (US)",

volume = "381",

pages = "1001--1030",

journal = "Communications In Mathematical Physics",

issn = "0010-3616",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

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

AU - Germain, Pierre

AU - Iwabuchi, Tsukasa

AU - Léger, Tristan

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.

UR - http://www.scopus.com/inward/record.url?scp=85096390161&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85096390161&partnerID=8YFLogxK

U2 - 10.1007/s00220-020-03919-6

DO - 10.1007/s00220-020-03919-6

M3 - Article

AN - SCOPUS:85096390161

SN - 0010-3616

VL - 381

SP - 1001

EP - 1030

JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 3

ER -

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

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this