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Growth rates for the linearized motion of fluid interfaces away from equilibrium

Publication ,  Journal Article
Beale, JT; Hou, TY; Lowengrub, JS
Published in: Communications on Pure and Applied Mathematics
January 1, 1993

We consider the motion of a two‐dimensional interface separating an inviscid, incompressible, irrotational fluid, influenced by gravity, from a region of zero density. We show that under certain conditions the equations of motion, linearized about a presumed time‐dependent solution, are wellposed; that is, linear disturbances have a bounded rate of growth. If surface tension is neglected, the linear equations are well‐posed provided the underlying exact motion satisfies a condition on the acceleration of the interface relative to gravity, similar to the criterion formulated by G. I. Taylor. If surface tension is included, the linear equations are well‐posed without qualifications, whether the fluid is above or below the interface. An interesting qualitative structure is found for the linear equations. A Lagrangian approach is used, like that of numerical work such as [3], except that the interface is assumed horizontal at infinity. Certain integral equations which occur, involving double layer potentials, are shown to be solvable in the present case. © 1993 John Wiley & Sons, Inc. Copyright © 1993 Wiley Periodicals, Inc., A Wiley Company

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Published In

Communications on Pure and Applied Mathematics

DOI

EISSN

1097-0312

ISSN

0010-3640

Publication Date

January 1, 1993

Volume

46

Issue

9

Start / End Page

1269 / 1301

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

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Beale, J. T., Hou, T. Y., & Lowengrub, J. S. (1993). Growth rates for the linearized motion of fluid interfaces away from equilibrium. Communications on Pure and Applied Mathematics, 46(9), 1269–1301. https://doi.org/10.1002/cpa.3160460903
Beale, J. T., T. Y. Hou, and J. S. Lowengrub. “Growth rates for the linearized motion of fluid interfaces away from equilibrium.” Communications on Pure and Applied Mathematics 46, no. 9 (January 1, 1993): 1269–1301. https://doi.org/10.1002/cpa.3160460903.
Beale JT, Hou TY, Lowengrub JS. Growth rates for the linearized motion of fluid interfaces away from equilibrium. Communications on Pure and Applied Mathematics. 1993 Jan 1;46(9):1269–301.
Beale, J. T., et al. “Growth rates for the linearized motion of fluid interfaces away from equilibrium.” Communications on Pure and Applied Mathematics, vol. 46, no. 9, Jan. 1993, pp. 1269–301. Scopus, doi:10.1002/cpa.3160460903.
Beale JT, Hou TY, Lowengrub JS. Growth rates for the linearized motion of fluid interfaces away from equilibrium. Communications on Pure and Applied Mathematics. 1993 Jan 1;46(9):1269–1301.
Journal cover image

Published In

Communications on Pure and Applied Mathematics

DOI

EISSN

1097-0312

ISSN

0010-3640

Publication Date

January 1, 1993

Volume

46

Issue

9

Start / End Page

1269 / 1301

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics