1,721,008 research outputs found
Sharp ill-posedness result for the periodic Benjamin-Ono equation (ERRATUM : PAPER WITHDRAWN)
No full textERRATUM : This paper has been withdrawn by the author since there were errors in the calculus of the defect coefficient in Page 11. The corrected calculus gives actually zero which do not lead to a contradiction on the continuity of the flow-map of the Benjamin-Ono equation. The author warmly thank Professor Patrick Gérard for having pointing out this error to him.ERRATUM : This paper has been withdrawn by the author since there were errors in the calculus of the defect coefficient in Page 11. The corrected calculus gives actually zero which do not lead to a contradiction on the continuity of the flow-map of the Benjamin-Ono equation. The author warmly thank Professor Patrick Gérard for having pointing out this error to him. (We prove the discontinuity for the weak L^2(\T) -topology of the flow-map associated with the periodic Benjamin-Ono equation. This ensures that this equation is ill-posed in H^s(\T) as soon as and thus completes exactly the well-posedness result obtained by the author.
Global attractor and asymptotic smoothing effects for the weakly damped cubic Schrödinger equation in L^2(\T)
No full textCorrected version. To appear in Dynamics of Partial Differential EquationsInternational audienceWe prove that the weakly damped cubic Schrödinger flow in L^2(\T) provides a dynamical system that possesses a global attractor. The proof relies on a sharp study of the behavior of the associated flow-map with respect to the weak L^2(\T) -convergence inspired by a previous work of the author. Combining the compactness in L^2(\T) of the attractor with the approach developed by Goubet, we show that the attractor is actually a compact set of H^2(\T) . This asymptotic smoothing effect is optimal in view of the regularity of the steady states
Global attractor and asymptotic smoothing effects for the weakly damped cubic Schrödinger equation in L^2(\T)
No full textCorrected version. To appear in Dynamics of Partial Differential EquationsInternational audienceWe prove that the weakly damped cubic Schrödinger flow in L^2(\T) provides a dynamical system that possesses a global attractor. The proof relies on a sharp study of the behavior of the associated flow-map with respect to the weak L^2(\T) -convergence inspired by a previous work of the author. Combining the compactness in L^2(\T) of the attractor with the approach developed by Goubet, we show that the attractor is actually a compact set of H^2(\T) . This asymptotic smoothing effect is optimal in view of the regularity of the steady states
Long time behaviour of some dispersive partial differential equations (PDEs)
No full textDans cette thèse on étudie la stabilité orbitale des ondes solitaires de deux types d’équations d’évolution non linéaires: l’équation de Degasperis-Procesi (DP), qui est une équation du type Camassa-Holm, et l’équation de Kawahara généralisée (gKW), qui correspond à une équation de Korteweg-de Vries généralisée (gKdV) supplémentée d’un terme d’ordre 5. Sur le modèle DP on apporte une amélioration significative de la preuve de la stabilité d’un peakon donnée par Lin et Liu. Puis, en utilisant la méthode de Martel-Merle-Tsai adaptée par El Dika-Molinet dans le cas de l’équation de Camassa-Holm, on montre que la somme de N peakons, de vitesses croissantes et suffisamment distants les uns des autres à l’instant initial, est orbitalement stable. Sur le modèle de Kawahara généralisé, on prouve l’existence de deux branches d’ondes solitaires : l’une construite en appliquant le théorème des fonctions implicites au voisinage d’une onde solitaire explicite de gKW découverte par Dey. al., l’autre construite en résolvant un problème de minimisation sur R, avec une contrainte qui force la famille à converger vers le soliton explicite de l’équation de Korteweg-de Vries généralisée (gKdV) lorsque le coefficient devant l’opérateur d’ordre 5 tend vers 0. Par remise à l’échelle, on obtient ainsi une branche constituée d’ondes solitaires voyageant à faibles vitesses. On prouve ensuite que les ondes solitaires constituant ces deux branches sont orbitalement stables en appliquant la méthode spectrale introduite par Benjamin et des arguments de continuité.No summary availabl
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Qualitative study of dispersive models
No full textDans cette thèse nous nous intéressons aux propriétés qualitatives des solutions de quelques équations d’ondes en milieux dispersifs ou dispersifs-dissipatifs. Dans le premier chapitre, nous étudions l’explosion de solutions dans le régime log-log et l’existence globale pour le problème de Cauchy de l’équation de Schrödinger L2-critique amortie. Dans un second chapitre, nous considérons l’équation de Schrödinger L2-critique avec un amortissement non linéaire. Selon la puissance du terme d’amortissement, nous montrons l’existence globale ou l’explosion en régime log-log. Dans le troisième chapitre, nous étudions le problème de Cauchy pour l’équation de Kadomtsev-Petviashvili-Burgers-I (KPBI) en deux dimensions,nous montrons que le problème est localement bien posé dans Hs(R2) pour tout s > -½, et que l’existence est globale dans L2(R2) sans aucune condition sur la donnée initiale. Dans le dernier chapitre, nous considèrons l’équation d’Ostrovsky sur le cercle, et nous construisons des mesures invariantes par le flot selon les quantitées conservées par cette équation.This thesis deals with the qualitative properties of solutions to some wave equations in dispersive or dispersive-dissipative media. In the first chapter, we study the blowup in the log-log regime and global existence of solutions to the Cauchy problem for the L2-critical damped nonlinear Schrödinger equation. In the second chapter, we consider the Cauchy problem for the L2-critical nonlinear Schrödinger equation with a nonlinear damping. According to the power of the damping term, we prove the global existence or the existence of finite time blowup dynamics with a log-log blow-up law. In the third chapter, we study the Cauchy problem for the Kadomtsev-Petviashvili-Burgers-I (KPBI) equations in two dimensions. We show that the problem is locally and globally well posed in Hs(R2) for any s > -½ , and that the existence is global in L2(R2) without any condition on the initial data. In the last chapter, we consider the Ostrovsky equation on the circle. We construct invariant measures under the flow for the conserved quantities of the equation
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Local and asymptotic analysis for some longwave approximations of fluid dynamics equations
No full textCette thèse est composée de deux parties indépendantes. Dans la première partie, nous étudions la stabilité orbitale et asymptotique de certaines ondes solitaires pointues (appelées peakons) de l'équation de Novikov. Dans la seconde partie, nous étudions le caractère bien posé local et global pour certaines équations de type Korteweg-de Vries en dimension un et deux, lorsqu'on pose le problème autour d'une fonction bornée sans décroissance spatiale particulière.L'équation de Novikov est une généralisation d'ordre supérieur de l'équation de Camassa-Holm. Elle possède une non-linéarité cubique, est complètement intégrable et conserve toutes les propriétés intéressantes (physiquement pertinentes) de l'équation de Camassa-Holm. Pour cette équation nous commençons par revisiter les résultats déjà connus de stabilité orbitale des peakons et nous établissons celle des multi-peakons. Puis, motivé par l'approche développée pour l'équation de Camassa-Holm, nous montrons la stabilité asymptotique des peakons et des multi-peakons de l'équation de Novikov. Pour cela nous introduisons en particulier une nouvelle fonctionnelle de Lyapunov qui peut être adaptée à un grand nombre de généralisations de Camassa-Holm d'ordre supérieur.Les équations Korteweg-de Vries généralisées et l'équation de Zakharov-Kuznetsov sont des modèles asymptotiques classiques respectivement uni et bi-dimensionels pour la propagation d'ondes longues dans un milieu dispersif ayant une réponse non linéaire.Nous étudions le caractère bien posé local et global dans ''l'espace d'énergie" de ces équations dans un contexte assez général, où nous permettons à la solution d'évoluer autour d'une fonction bornée ��. Cela nous permet de fournir un cadre afin étudier l'évolution temporelle des perturbations localisées de kinks, ainsi que des perturbations localisées des solutions périodiques de chacune de ces équations. Les approches classiques basées sur une utilisation du théorème du point fixe de Banach ne peuvent pas aboutir dans cette configuration du fait de la perte d'une dérivée due à l'introduction de la fonction ��. Nous sommes donc amenés à nous tourner vers des raffinements de la méthode d'énergie. Nous utilisons deux approches différentes selon la dimension. La première approche repose sur une méthode introduite par Molinet-Vento qui utilise le caractàre fortement non résonant de l'équation de Korteweg-de Vries classique. Elle est de ce fait moins bien adaptée aux dimensions supérieures mais à l'avantage de donner en plus l'unicité inconditionnelle (unicité des solutions faibles). La deuxième approche repose sur l'utilisation des espaces Bourgain en temps courts, développée en particulier par Ionescu, Kenig et Tataru. Ici un choix approprié du rapport entre la longueur des petits intervalles de temps et l'inverse de la fréquence spatiale permet entre autre de rattraper la perte de dérivée.This thesis is composed of two independent parts. In the first part, we study the orbital and asymptotic stability of certain peaked solitary waves (peakons) of the Novikov equation. In the second part, we study the local and global well-posedness for certain Korteweg-de Vries type equations in dimensions one and two, when the problem is posed in the background of a bounded function without any particular spatial decay.The Novikov equation is a higher-order generalization of the Camassa-Holm equation. It has a cubic nonlinearity, is completely integrable, and keeps all the interesting (physically relevant) properties of the Camassa-Holm equation. For this equation, we start by revisiting the already known orbital stability results for peakons, and we establish the corresponding result for multi-peakons. Then, motivated by the approach developed for the Camassa-Holm equation, we show the asymptotic stability of peakons and multi-peakons of the Novikov equation. With this aim, we introduce in particular a new Lyapunov functional, which can be adapted to a large number of higher-order generalizations of the Camassa-Holm equation.The generalized Korteweg-de Vries equations and the Zakharov-Kuznetsov equation are classical asymptotic models, in dimensions one and two respectively, for the propagation of long waves in a dispersive medium with a nonlinear response. We study the local and global well-posedness of these equations in the "energy space", in a rather general context, where we allow the solution to evolve in the background of a bounded function ��. These results provide a framework for studying the time evolution of localized perturbations of Kinks, as well as localized non-periodic perturbations of periodic solutions for each of these equations. Classical approaches based on the use of Banach's fixed point theorem cannot succeed in the present configuration due to the loss of a derivative due to the introduction of the non-integrable background function ��. Thus, we are led to turn to refinements of the energy method. We use two different approaches depending on whether we are on the one- or two-dimensional case. The first approach is based on a method introduced by Molinet-Vento which uses the strongly non-resonant character of the classical Korteweg-de Vries equation. This method is not well suited to higher dimensional problems but has the advantage of providing, in addition, the unconditional uniqueness of solutions (uniqueness of weak solutions). The second approach is based on the use of short-time Bourgain spaces, introduced for the first time by Ionescu, Kenig, and Tataru. Here, an appropriate choice of the relationship between the length of the time intervals and the inverse of the spatial frequency allows us, among other things, to recover the derivative loss
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