### 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 language | English (US) |
---|---|

Pages (from-to) | 157-166 |

Number of pages | 10 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 38 |

Issue number | 2 |

DOIs | |

State | Published - 1985 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications on Pure and Applied Mathematics*,

*38*(2), 157-166. https://doi.org/10.1002/cpa.3160380203

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

Research output: Contribution to journal › Article

*Communications on Pure and Applied Mathematics*, vol. 38, no. 2, pp. 157-166. https://doi.org/10.1002/cpa.3160380203

}

TY - JOUR

T1 - Global existence for a nonlinear theory of bubbly liquids

AU - Caflisch, Russel

PY - 1985

Y1 - 1985

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84990619115&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84990619115&partnerID=8YFLogxK

U2 - 10.1002/cpa.3160380203

DO - 10.1002/cpa.3160380203

M3 - Article

VL - 38

SP - 157

EP - 166

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 2

ER -