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

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

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

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