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Radiation conditions at the top of a rotational cusp in the theory of water-waves

Sergey A. Nazarov, Jari Taskinen (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We study the linearized water-wave problem in a bounded domain (e.g.a finite pond of water) of ℝ 3 , having a cuspidal boundary irregularity created by a submerged body. In earlier publications the authors discovered that in this situation the spectrum of the problem may contain a continuous component in spite of the boundedness of the domain. Here, we proceed to impose and study radiation conditions at a point 𝒪 of the water surface, where a submerged body touches the surface (see Fig. 1). The radiation...

Radiation conditions at the top of a rotational cusp in the theory of water-waves

Sergey A. Nazarov, Jari Taskinen (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

We study the linearized water-wave problem in a bounded domain (e.g. a finite pond of water) of ℝ 3 , having a cuspidal boundary irregularity created by a submerged body. In earlier publications the authors discovered that in this situation the spectrum of the problem may contain a continuous component in spite of the boundedness of the domain. Here, we proceed to impose and study radiation conditions at a point 𝒪 of the water surface, where a submerged body touches the surface (see Fig. 1)....

Radiation fields

Piotr T. Chruściel, Olivier Lengard (2005)

Bulletin de la Société Mathématique de France

We study the “hyperboloidal Cauchy problem” for linear and semi-linear wave equations on Minkowski space-time, with initial data in weighted Sobolev spaces allowing singular behavior at the boundary, or with polyhomogeneous initial data. Specifically, we consider nonlinear symmetric hyperbolic systems of a form which includes scalar fields with a λ φ p nonlinearity, as well as wave maps, with initial data given on a hyperboloid; several of the results proved apply to general space-times admitting conformal...

RBF Based Meshless Method for Large Scale Shallow Water Simulations: Experimental Validation

Y. Alhuri, A. Naji, D. Ouazar, A. Taik (2010)

Mathematical Modelling of Natural Phenomena

2D shallow water equations with depth-averaged k−ε model is considered. A meshless method based on multiquadric radial basis functions is described. This methods is based on the collocation formulation and does not require the generation of a grid and any integral evaluation. The application of this method to a flow in horizontal channel, taken as an experimental device, is presented. The results of computations are compared with experimental data...

Reaction-diffusion-convection problems in unbounded cylinders.

Rozenn Texier-Picard, Vitaly A. Volpert (2003)

Revista Matemática Complutense

The work is devoted to reaction-diffusion-convection problems in unbounded cylinders. We study the Fredholm property and properness of the corresponding elliptic operators and define the topological degree. Together with analysis of the spectrum of the linearized operators it allows us to study bifurcations of solutions, to prove existence of convective waves, and to make some conclusions about their stability.

Recent developments on wall-bounded turbulence.

Javier Jiménez (2007)

RACSAM

The study of turbulence near walls has experienced a renaissance in the last decade, in part because of the availability of high-quality numerical simulations. The viscous and buffer layers over smooth walls are now fairly well understood. They are essentially independent of the outer flow, and there is a family of numerically-exact nonlinear structures that predict well many of the best-known characteristics of the wall layer, such as the intensity and the spectra of the velocity fluctuations,...

Recent results on the Boltzmann equation

Carlo Cercignani (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In the last few years the theory of the nonlinear Boltzmann equation has witnessed a veritable turrent of contributions, spurred by the basic result of DiPerna and Lions. Here we wish to survey these results with particular attention to some recent developments.

Reduced basis method for finite volume approximations of parametrized linear evolution equations

Bernard Haasdonk, Mario Ohlberger (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

The model order reduction methodology of reduced basis (RB) techniques offers efficient treatment of parametrized partial differential equations (P2DEs) by providing both approximate solution procedures and efficient error estimates. RB-methods have so far mainly been applied to finite element schemes for elliptic and parabolic problems. In the current study we extend the methodology to general linear evolution schemes such as finite volume schemes for parabolic and hyperbolic evolution equations....

Reduced resistive MHD in Tokamaks with general density

Bruno Després, Rémy Sart (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The aim of this paper is to derive a general model for reduced viscous and resistive Magnetohydrodynamics (MHD) and to study its mathematical structure. The model is established for arbitrary density profiles in the poloidal section of the toroidal geometry of Tokamaks. The existence of global weak solutions, on the one hand, and the stability of the fundamental mode around initial data, on the other hand, are investigated.

Reduced resistive MHD in Tokamaks with general density

Bruno Després, Rémy Sart (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

The aim of this paper is to derive a general model for reduced viscous and resistive Magnetohydrodynamics (MHD) and to study its mathematical structure. The model is established for arbitrary density profiles in the poloidal section of the toroidal geometry of Tokamaks. The existence of global weak solutions, on the one hand, and the stability of the fundamental mode around initial data, on the other hand, are investigated.

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