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)
Journal	Communications In Mathematical Physics
DOIs	https://doi.org/10.1007/s00220-020-03919-6
State	Accepted/In press - 2020

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s00220-020-03919-6

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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 = "Funding Information: P. Germain was partially supported by the NSF Grant DMS-1501019. T. Iwabuchi was supported by JSPS KAKENHI Grant 17H04824. ",

year = "2020",

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

language = "English (US)",

journal = "Communications in Mathematical Physics",

issn = "0010-3616",

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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.

PY - 2020

Y1 - 2020

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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