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pro vyhledávání: '"76b15"'
We study the formation of singularities in the Camassa-Holm (CH) equation, providing a detailed description of the blow-up dynamics and identifying the precise H\"older regularity of the gradient blow-up solutions. To this end, we first construct sel
Externí odkaz:
http://arxiv.org/abs/2412.00558
The Klein-Gordon-Boussinesq (KGB) system is proposed in the literature as a model problem to study the validity of approximations in the long wave limit provided by simpler equations such as KdV, nonlinear Schr\"{o}dinger or Whitham equations. In thi
Externí odkaz:
http://arxiv.org/abs/2411.18173
Autor:
Avramenko, Olga, Naradovyi, Volodymyr
The propagation of internal waves in a hydrodynamic system comprising a solid bottom and an upper half-space is investigated. The study is conducted within the framework of a nonlinear low-dimensional model incorporating surface tension on an interfa
Externí odkaz:
http://arxiv.org/abs/2411.15168
Autor:
Curtin, Conor, Ivanov, Rossen
Publikováno v:
Wave Motion 129 (2024) 103343
The currents in the ocean have a serious impact on ocean dynamics, since they affect the transport of mass and thus the distribution of salinity, nutrients and pollutants. In many physically important situations the current depends quadratic-ally on
Externí odkaz:
http://arxiv.org/abs/2410.15209
Autor:
Wan, Lizhe
This article is devoted to the study of local well-posedness for deep water waves with constant vorticity in two space dimensions on the real line. The water waves can be paralinearized and written as a quasilinear dispersive system of equations. By
Externí odkaz:
http://arxiv.org/abs/2410.11762
Autor:
Wan, Lizhe
The study of gravity-capillary water waves in two space dimensions has been an important question in mathematical fluid dynamics. By implementing the cubic modified energy method of Ifrim-Tataru in the context of gravity-capillary waves, we show that
Externí odkaz:
http://arxiv.org/abs/2410.05201
Autor:
Du, Lili, Yang, Chunlei
In 1880, Stokes examined an incompressible irrotational periodic traveling water wave under the influence of gravity and conjectured the existence of an extreme wave with a corner of $120^{\circ}$ at the crest. The first rigorous proof of the conject
Externí odkaz:
http://arxiv.org/abs/2410.04178
Autor:
Ivanov, Rossen I.
Publikováno v:
Henry, D. (ed.) Nonlinear Dispersive Waves. Advances in Mathematical Fluid Mechanics, Birkh\"auser, Cham, 2024; pp 81-97
A single incompressible, inviscid, irrotational fluid medium bounded above by a free surface is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface waves are pres
Externí odkaz:
http://arxiv.org/abs/2409.03091
We prove that all irrotational planar periodic traveling waves of sufficiently small-amplitude are spectrally unstable as solutions to three-dimensional inviscid finite-depth gravity water-waves equations.
Comment: 29 pages, 1 figure
Comment: 29 pages, 1 figure
Externí odkaz:
http://arxiv.org/abs/2409.01663
We provide the first construction of overhanging gravity water waves having the approximate form of a disk joined to a strip by a thin neck. The waves are solitary with constant vorticity, and exist when an appropriate dimensionless gravitational con
Externí odkaz:
http://arxiv.org/abs/2409.01182