Global existence for a nonlinear theory of bubbly liquids

Russel Caflisch

Research output: Contribution to journalArticle

Abstract

Global existence of smooth solutions is proved for an effective theory of bubbly liquids for either the initial value problem or initial boundary value problem in one dimension. This shows that the theory does not describe shock waves or bubble collapse. Since the analysis is not for the steady boundary value problem, there is no discussion of resonance. The proof uses a semilinear form of the equations to get local existence. A priori bounds resulting from energy conservation and a nonlinear Gronwall‐like inequality are then derived to prove global existence.

Original languageEnglish (US)
Pages (from-to)157-166
Number of pages10
JournalCommunications on Pure and Applied Mathematics
Volume38
Issue number2
DOIs
StatePublished - 1985

Fingerprint

Global Existence
Boundary value problems
Liquid
A Priori Bounds
Initial value problems
Local Existence
Energy Conservation
Liquids
Smooth Solution
Shock Waves
Semilinear
Shock waves
Initial-boundary-value Problem
Bubble
One Dimension
Initial Value Problem
Energy conservation
Boundary Value Problem
Form

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Global existence for a nonlinear theory of bubbly liquids. / Caflisch, Russel.

In: Communications on Pure and Applied Mathematics, Vol. 38, No. 2, 1985, p. 157-166.

Research output: Contribution to journalArticle

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