1,720,978 research outputs found
Loss of Regularity for the 2D Euler Equations
No full textIn this note, we construct solutions to the 2D Euler equations which belong to the Yudovich class but lose W-1,W-p regularity continuously with time.Y
Classical solutions for fractional porous medium flow
No full textWe consider the fractional porous medium flow introduced by Caffarelli and Vazquez (2011) and obtain local in time existence, uniqueness, and blow-up criterion for smooth solutions. The proof is based on establishing a commutator estimate involving fractional Laplacian operators. (C) 2021 Elsevier Ltd. All rights reserved.Y
On the Cauchy Problem for the Hall and Electron Magnetohydrodynamic Equations Without Resistivity I: Illposedness Near Degenerate Stationary Solutions
No full text© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.In this article, we prove various illposedness results for the Cauchy problem for the incompressible Hall- and electron-magnetohydrodynamic (MHD) equations without resistivity. These PDEs are fluid descriptions of plasmas, where the effect of collisions is neglected (no resistivity), while the motion of the electrons relative to the ions (Hall current term) is taken into account. The Hall current term endows the magnetic field equation with a quasilinear dispersive character, which is key to our mechanism for illposedness. Perhaps the most striking conclusion of this article is that the Cauchy problems for the Hall-MHD (either viscous or inviscid) and the electron-MHD equations, under one translational symmetry, are ill-posed near the trivial solution in any sufficiently high regularity Sobolev space Hs and even in any Gevrey spaces. This result holds despite obvious wellposedness of the linearized equations near the trivial solution, as well as conservation of the nonlinear energy, by which the L2 norm (energy) of the solution stays constant in time. The core illposedness (or instability) mechanism is degeneration of certain high frequency wave packet solutions to the linearization around a class of linearly degenerate stationary solutions of these equations, which are essentially dispersive equations with degenerate principal symbols. The method developed in this work is sharp and robust, in that we also prove nonlinear Hs-illposedness (for s arbitrarily high) in the presence of fractional dissipation of any order less than 1, matching the previously known wellposedness results. The results in this article are complemented by a companion work, where we provide geometric conditions on the initial magnetic field that ensure wellposedness(!) of the Cauchy problems for the incompressible Hall and electron-MHD equations. In particular, in stark contrast to the results here, it is shown in the companion work that the nonlinear Cauchy problems are well-posed near any nonzero constant magnetic field.N
Filamentation near Hill's vortex
No full textFor the axi-symmetric incompressible Euler equations, we prove linear in time filamentation near Hill's vortex: there exists an arbitrary small outward perturbation growing linearly for all times. This is based on combining the recent nonlinear orbital stability obtained by the first author with a dynamical bootstrapping scheme for particle trajectories. These results rigorously confirm numerical simulations by Pozrikidis in 1986
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe 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
Variations on the Author
Full text link“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
Full text linkWe 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
Dynamics of the incompressible Euler equations at critical regularity
No full textThe purpose of this work is to study the incompressible Euler equations in scaling critical spaces, the function spaces which are left invariant under the natural scaling transformations for the Euler equations. We demonstrate that under appropriate symmetry assumptions, which depends on the dimension of the physical space, the Euler equations are well-posed in certain critical spaces.
It turns out that such critical spaces contain solutions which are radially homogeneous, whose dynamics is necessarily described by a system of one less dimension. In the case of 2D Euler equation, we obtain from this procedure a new 1D fluid model, and it turns out that the long-time dynamics of this model can be analyzed under some mild assumptions on the initial data.
We proceed to show well-posedness results of ``hybrid type'', by which we mean that if the initial data consists of a radially homogeneous piece and a smooth piece vanishing at the origin, the solution continues to have this decomposition, with the homogeneous part solving the lower dimensional system. As an immediate consequence, we obtain a conditional blow-up result, which states that if there is a finite time singularity for the 2D model arising from the 3D Euler equations, then there is a finite time blow-up for a Lipschitz continuous solution of the 3D Euler equation with compact support and hence of finite energy.
As an application of the critical spaces introduced in this work, we obtain a global well-posedness result for a certain class of singular vortex patches in two dimensions
Inviscid damping phenomena in some fluid models
No full textInviscid damping phenomena in mathematical fluid dynamics have been intensively studied for the last decade, as the hydrodynamic analogue of Landau damping for the Vlasov equations. In its full generality, inviscid damping accounts for the extra stabilization mechanism that emerges near target steady states, within the fluid systems that are not inherently energy dissipative.
In Chapter 2, we introduce the 2D inviscid IPM (incompressible porous medium) equation and then prove the quantitative asymptotic stability of the quasi-linearly stratified densities in the IPM equation on the 2D whole space. The quantification is performed with respect to the intensity of stratification. Our proof robustly applies to other fundamental domains in the case of the purely linear density stratification; we prove the analogous results on the 2D torus and the horizontally periodic strip. The obtained temporal decay rates are all sharp, reaching the level of the linearized equations.
In Chapter 3 and Chapter 4, we generalize the concept of inviscid damping as the extra stabilizing mechanism that appears in the vicinity of certain stationary solutions to the fluid equations that are fully or at least partially non-dissipative. Such an encompassing notion allows us to view various phenomena through the window of inviscid damping. More precisely, we prove the Lyapunov stability of the nonzero constant background magnetic field for the non-resistive 2D MHD (magnetohydrodynamics) equations in Chapter 3. Then we investigate the validity of the QG (quasi-geostrophic) dynamics as the legit approximation for the inviscid rotating stratified Boussinesq flows in Chapter 4; we determine between convergence and non-convergence with respect to the rotation-stratification ratio.Science, Faculty ofMathematics, Department ofGraduat
- …
