Global existence for a nonlinear theory of bubbly liquids

Russel E. Caflisch

Research output: Contribution to journalArticlepeer-review


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
Issue number2
StatePublished - Mar 1985

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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