نتایج جستجو برای: the benjamin ono equation

تعداد نتایج: 16078511  

Journal: :Journal of Differential Equations 2011

2008
SEBASTIAN HERR

Explicit counterexamples to bilinear estimates related to the Benjamin-Ono equation in the periodic setting are calculated for functions of zero mean value. As a consequence, certain bilinear estimates fail to hold in spite of the analyticity of the flow map. The latter has been shown recently by L. Molinet.

2017
Luc Molinet Didier Pilod LUC MOLINET

In a recent work [12], Ionescu and Kenig proved that the Cauchy problem associated to the Benjamin-Ono equation is well-posed in L(R). In this paper we give a simpler proof of Ionescu and Kenig’s result, which moreover provides stronger uniqueness results. In particular, we prove unconditional well-posedness in Hs(R), for s > 1 4 .

2003
TERENCE TAO

We show that the Benjamin-Ono equation is globally well-posed in H s (R) for s ≥ 1. This is despite the presence of the derivative in the non-linearity, which causes the solution map to not be uniformly continuous in H s for any s [15]. The main new ingredient is to perform a global gauge transformation which almost entirely eliminates this derivative.

Journal: :Proceedings of the American Mathematical Society 2019

1999
Beatrice Pelloni Vassilios A. Dougalis

We use a spectral method to solve numerically two nonlocal, nonlinear, dispersive, integrable wave equations, the Benjamin-Ono and the Intermediate Long Wave equations. The proposed numerical method is able to capture well the dynamics of the solutions; we use it to investigate the behaviour of solitary wave solutions of the equations with special attention to those, among the properties usuall...

Journal: :ESAIM: Control, Optimisation and Calculus of Variations 2005

2005
HENRIK KALISCH

The regularized Benjamin–Ono equation appears in the modeling of long-crested interfacial waves in two-fluid systems. For this equation, Fourier–Galerkin and collocation semi-discretizations are proved to be spectrally convergent. A new exact solution is found and used for the experimental validation of the numerical algorithm. The scheme is then used to study the interaction of two solitary wa...

Journal: :J. Nonlinear Science 2000
Beatrice Pelloni V. A. Dougalis

We use a spectral method to solve numerically two nonlocal, nonlinear, dispersive, integrable wave equations, the Benjamin-Ono and the Intermediate Long Wave equations. The proposed numerical method is able to capture well the dynamics of the solutions; we use it to investigate the behaviour of solitary wave solutions of the equations with special attention to those, among the properties usuall...

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