منابع مشابه
Extended Serre Equations for Applications in Intermediate Water Depths
The Serre or Green and Naghdi equations are fully-nonlinear and weakly dispersive and have a built-in assumption of irrotationality. However, like the standard Boussinesq equations, also Serre’s equations are only valid for long waves in shallow waters. To allow applications in a greater range of h0/l, where h0 and l represent, respectively, depth and wavelength characteristics, a new set of ex...
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We prove the weight elimination direction of the Serre weight conjectures as formulated by [Her09] for forms of U(n) which are compact at infinity and split at places dividing p in generic situations. That is, we show that all modular weights for a mod p Galois representation are contained in the set predicted by Herzig. Under some additional hypotheses, we also show modularity of all the “obvi...
متن کاملModel Equations for Gravity-capillary Waves in Deep Water
The Euler equations for water waves in any depth have been shown to have solitary wave solutions when the effect of surface tension is included. This paper proposes three quadratic model equations for these types of waves in infinite depth with a two-dimensional fluid domain. One model is derived directly from the Euler equations. Two further simpler models are proposed, both having the full gr...
متن کاملThird Order Semilinear Dispersive Equations Related to Deep Water Waves
ABSTRACT. We present local existence theorem of the initial value problem for third order semilinear dispersive partial differential equations in two space dimensions. This type of equations arises in the study of gravity wave of deep water, and cannot be solved by the classical energy method. To solve the initial value problem, we make full use of pseudodifferential operators with nonsmooth co...
متن کاملOn the Galerkin/Finite-Element Method for the Serre Equations
A highly accurate numerical scheme is presented for the Serre system of partial differential equations, which models the propagation of dispersive shallow water waves in the fully-nonlinear regime. The fully-discrete scheme utilizes the Galerkin / finiteelement method based on smooth periodic splines in space, and an explicit fourth-order Runge-Kutta method in time. Computations compared with e...
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ژورنال
عنوان ژورنال: Mathematical Modelling of Natural Phenomena
سال: 2017
ISSN: 1760-6101
DOI: 10.1051/mmnp/201712103