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Problems in the dynamics of flotation liquids
S. A. Gabov,A. G. Sveshnikov +1 more
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In this article, the authors present new mathematical results in the theory of linear and nonlinear waves on the surface of a flotation liquid, and prove the existence of nonlinear standing waves within the framework of an exact physical model.Abstract:
This survey presents new mathematical results in the theory of linear and nonlinear waves on the surface of a flotation liquid. A flotation liquid is a liquid on whose surface heavy particles are floating; the particles may consist of arbitrary materials or may be particles of frozen liquid. The first part of the article considers initial- and boundary-value problems in the theory, their solvability, and the behavior of the solutions over long periods. In the second part of the survey, theorems are proved on the existence of nonlinear standing waves within the framework of an exact physical model, and both internal and free waves are considered. Also, the fundamental equations for shallow flotation waves are derived and examined.read more
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Journal ArticleDOI
Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).
TL;DR: To the best of our knowledge, there is only one application of mathematical modelling to face recognition as mentioned in this paper, and it is a face recognition problem that scarcely clamoured for attention before the computer age but, having surfaced, has attracted the attention of some fine minds.
Journal ArticleDOI
Oscillations of Stratified Liquid Partially Covered by Crumpling Ice
TL;DR: In this paper, the authors study the problem on small motions of ideal stratified fluid with a free surface, partially covered by crumbling ice, and find sufficient existence conditions for existence of a strong (with respect to the time variable) solution to the initial-boundary value problem describing evolution of the specified hydrodynamics system.
Малые движения системы идеальныхстратифицированных жидкостей, полностьюпокрытой крошеным льдом
TL;DR: In this article, the authors studied the problem of small motions of two non-mixing ideal stratified fluids with a free surface, covered with crumbling ice, and found sufficient existence conditions for a strong (with respect to the time variable) solution of the initial-boundary value problem describing the evolution of the specified hydrodynamics system.
Journal ArticleDOI
Oscillations of a Stratified Liquid Partially Covered with Ice (General Case)
TL;DR: In this paper, the authors studied the problem of small motions of an ideal stratified liquid whose free surface consists of three regions: liquid surface without ice, a region of elastic ice, and an area of crumbled ice.
Journal ArticleDOI
On the coupled time-harmonic motion of a freely floating body and water covered by brash ice
TL;DR: In this article, the authors considered a mechanical system consisting of water covered by brash ice and a body freely floating near equilibrium, where the water occupies a half-space into which an infinitely long surface-piercing cylinder is immersed, thus allowing us to study two-dimensional modes of the coupled motion, which is assumed to be of small amplitude.
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Book
Linear and Nonlinear Waves
TL;DR: In this paper, a general overview of the nonlinear theory of water wave dynamics is presented, including the Wave Equation, the Wave Hierarchies, and the Variational Method of Wave Dispersion.
Journal ArticleDOI
Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).
TL;DR: To the best of our knowledge, there is only one application of mathematical modelling to face recognition as mentioned in this paper, and it is a face recognition problem that scarcely clamoured for attention before the computer age but, having surfaced, has attracted the attention of some fine minds.