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Lannes, David  WPI, OMP 1, Seminar Room 08.135  Tue, 19. Sep 17, 9:30 
The shoreline problem for the nonlinear shallow water and GreenNaghdi equations  
The nonlinear shallow water equations and the GreenNaghdi equations are the most commonly used models to describe coastal flows. A natural question is therefore to investigate their behavior at the shoreline, i.e. when the water depth vanishes. For the nonlinear shallow water equations, this problem is closely related to the vacuum problem for compressible Euler equations, recently solved by JangMasmoudi and CoutandShkoller. For the GreenNaghdi equation, the analysis is of a different nature due to the presence of linear and nonlinear dispersive terms. We will show in this talk how to address this problem.  

Ehrnstrom, Mats  WPI, OMP 1, Seminar Room 08.135  Tue, 19. Sep 17, 11:00 
Smallamplitude solitary waves for the fulldispersion KadomtsevPetviashvili equation  
Using constrained minimisation and a decomposition in Fourier space, we prove that the KadomtsevPetviashvili (KPI) equation modified with the exact dispersion relation from the gravitycapillary waterwave problem admits a family of small solitary solutions, approximating these of the standard KPI equation. The KPI equation, as well as its fully dispersive counterpart, describes gravitycapillary waves with strong surface tension. This is joint work with Mark Groves, Saarbrücken  

Duchêne, Vincent  WPI, OMP 1, Seminar Room 08.135  Tue, 19. Sep 17, 14:30 
A full dispersion model for the propagation of long gravity waves  
We will motivate and study a model for the propagation of surface gravity waves, which can be viewed as a fully nonlinear bidirectional Whitham equation. This model belongs to a family of systems of GreenNaghdi type with modified frequency dispersion. We will discuss the wellposedness of such systems, as well as the existence of solitary waves. The talk will be based on a work in collaboration with Samer Israwi and Raafat Talhouk (Beirut) and another in collaboration with Dag Nilsson and Erik Wahlén (Lund)  

Groves, Mark  WPI, OMP 1, Seminar Room 08.135  Wed, 20. Sep 17, 9:30 
Fully localised solitary gravitycapillary water waves (joint work with B. Buffoni and E. Wahlén)  
We consider the classical gravitycapillary waterwave problem in its usual formulation as a threedimensional freeboundary problem for the Euler equations for a perfect fluid. A solitary wave is a solution representing a wave which moves in a fixed direction with constant speed and without change of shape; it is fully localised if its profile decays to the undisturbed state of the water in every horizontal direction. The existence of fully localised solitary waves has been predicted on the basis of simpler model equations, namely the KadomtsevPetviashvili (KP) equation in the case of strong surface tension and the DaveyStewartson (DS) system in the case of weak surface tension. In this talk we confirm the existence of such waves as solutions to the full waterwave problem and give rigorous justification for the use of the model equations.  

Burtea, Cosmin  WPI, OMP 1, Seminar Room 08.135  Wed, 20. Sep 17, 11:00 
Long time existence results for the abcd Bousssinesq systems  
In this talk we will review some long time existence results for the abcdBoussinesq systems. We will discuss both the Sobolev and the nonlocalized, boretype initial data cases. The main idea in order to get a priori estimates is to symmetrize the family of systems of equations verified by the frequencies of magnitude 2^{j} of the unknowns for each j¡Ý0. For the boretype case, an additional decomposition of the initial data into lowhigh frequencies is needed in order to tackle the infiniteenergy aspect of these kind of data.  

Iguchi, Tatsuo  WPI, OMP 1, Seminar Room 08.135  Wed, 20. Sep 17, 14:00 
IsobeKakinuma model for water waves as a higher order shallow water approximation  
We justify rigorously an IsobeKakinuma model for water waves as a higher order shallow water approximation in the case of a flat bottom. It is known that the full water wave equations are approximated by the shallow water equations with an error of order $delta^2$, where $delta$ is a small nondimensional parameter defined as the ratio of the typical wavelength to the mean depth. The GreenNaghdi equations are known as higher order approximate equations to the water wave equations with an error of order $delta^4$. In this talk I report that the IsobeKakinuma model is a much higher approximation to the water wave equations with an error of order $delta^6$.  

Rousset, Frederic  WPI, OMP 1, Seminar Room 08.135  Wed, 20. Sep 17, 15:30 
Large time behavior of asymptotic models for waterwaves  
We will discuss modified scattering properties, for small Solutions and/or in the vicinity of a solitary waves for model dispersive equations in dimension one. We will mainly focus on the modified Korteweg de Vries equation and the cubic Nonlinear Schrodinger equation with potential. Joint works with P. Germain and F. Pusateri.  

Haspot, Boris  WPI, OMP 1, Seminar Room 08.135  Thu, 21. Sep 17, 9:30 
Global wellposedness of the EulerKorteweg system for small irrotational data  
The EulerKorteweg equations are a modification of the Euler equations that takes into account capillary effects. In the general case they form a quasilinear system that can be recast as a degenerate Schr ̈odinger type equation. Local wellposedness (in subcritical Sobolev spaces) was obtained by BenzoniDanchinDescombes in any space dimension, however, except in some special case (semilinear with particular pressure) no global well posedness is known. We prove here that under a natural stability condition on the pressure, global wellposedness holds in dimension d ¡Ý 3 for small irrotational initial data. The proof is based on a modified energy estimate, standard dispersive properties if d ¡Ý 5, and a careful study of the nonlinear structure of the quadratic terms in dimension 3 and 4 involving the theory of space time resonance.  

Klein, Christian  WPI, OMP 1, Seminar Room 08.135  Thu, 21. Sep 17, 11:00 
Numerical study of PDEs with nonlocal dispersion  

Barros, Ricardo  WPI, OMP 1, Seminar Room 08.135  Thu, 21. Sep 17, 14:30 
Large amplitude internal waves in threelayer flows  
Large amplitude internal waves in a threelayer flow confined between two rigid walls will be examined in this talk. The mathematical model under consideration arises as a particular case of the multilayer model proposed by Choi (2000) and is an extension of the twolayer MCC (MiyataChoiCamassa) model. The model can be derived without imposing any smallness assumption on the wave amplitudes and is wellsuited to describe internal waves within a strongly nonlinear regime. We will investigate its solitarywave solutions and unveil some of their properties by carrying out a critical point analysis of the underlying dynamical system.  

Saut, JeanClaude  WPI, OMP 1, Seminar Room 08.135  Fri, 22. Sep 17, 9:30 
Existence of solitary waves for internal waves in twolayers systems  
We establish the existence of solitary waves for two classes of twolayers systems modeling the propagation of internal waves. More precisely we consider the BoussinesqFull dispersion system and the Intermediate Long Wave (ILW) system together with its BenjaminOno (B0) limit. This is work in progress with Jaime Angulo Pava (USP)  

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