On similarity flows for the compressible Euler system

Helge Kristian Jenssen, Charis Tsikkou

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Radial similarity flow offers a rare instance where concrete inviscid, multi-dimensional, compressible flows can be studied in detail. In particular, there are flows of this type that exhibit imploding shocks and cavities. In such flows, the primary flow variables (density, velocity, pressure, and temperature) become unbounded at the time of collapse. In both cases, the solution can be propagated beyond collapse by having an expanding shock wave reflect off the center of motion. These types of flows are of relevance in bomb-making and inertial confinement fusion and also as benchmarks for computational codes; they have been investigated extensively in the applied literature. However, despite their obvious theoretical interest as examples of unbounded solutions to the multi-dimensional Euler system, the existing literature does not address to what extent such solutions are bona fide weak solutions. In this work, we review the construction of globally defined radial similarity shock and cavity flows and give a detailed description of their behavior following collapse. We then prove that similarity shock solutions provide genuine weak solutions, of unbounded amplitude, to the multi-dimensional Euler system. However, both types of similarity flows involve regions of vanishing pressure prior to collapse (due to vanishing temperature and vacuum, respectively) - raising the possibility that Euler flows may remain bounded in the absence of such regions.

Original languageEnglish (US)
Article number121507
JournalJournal of Mathematical Physics
Volume59
Issue number12
DOIs
StatePublished - Dec 1 2018

Fingerprint

Euler System
Shock
Multidimensional Systems
shock
Weak Solution
Cavity Flow
Unbounded Solutions
cavity flow
Compressible Flow
compressible flow
Similarity
inertial confinement fusion
Shock Waves
Euler
Fusion
Vacuum
Cavity
shock waves
Benchmark
Motion

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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On similarity flows for the compressible Euler system. / Jenssen, Helge Kristian; Tsikkou, Charis.

In: Journal of Mathematical Physics, Vol. 59, No. 12, 121507, 01.12.2018.

Research output: Contribution to journalArticle

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