Forward Discretely Self-Similar Solutions of the MHD Equations and the Viscoelastic Navier-Stokes Equations with Damping

In this paper, we prove the existence of forward discretely self-similar solutions to the MHD equations and the viscoelastic Navier-Stokes equations with damping with large weak $L^3$ initial data. The same proving techniques are also applied to construct self-similar solutions to the MHD equations and the viscoelastic Navier-Stokes equations with damping with large weak $L^3$ initial data. This approach is based on [Z. Bradshaw and T.-P. Tsai, Ann. Henri Poincar'{e}, vol. 18, no. 3, 1095-1119, 2017]

Mathematical Aspects of Hydrodynamics

The workshop dealt with the partial differential equations that describe fluid motion and related topics. These topics included both inviscid and viscous fluids in two and three dimensions. Some talks addressed aspects of fluid dynamics such as the construction of wild weak solutions, compressible shock formation, inviscid limit and behavior of boundary layers, as well as both polymer/fluid and structure/fluid interaction

Magnetic Characterization of Fischer-Tropsch Catalysts

INGENIERIE+JDAInternational audienceThis paper reviews recent developments in the application of magnetic methods for investigation of Fischer-Tropsch catalysts involving cobalt, iron and nickel. Magnetic characterization provides valuable information about catalyst reduction, sizes of ferromagnetic nanoparticles, chemisorption on ferromagnetics and topochemical reactions which occur with the catalysts during the genesis of the active phase and in the conditions of Fischer-Tropsch synthesis. The capabilities and challenges of the magnetic methods are discussed.Cet article passe en revue les développements récents dans le domaine de la caractérisation des catalyseurs Fischer-Tropsch à base de cobalt, de fer et de nickel par la méthode magnétique. La caractérisation magnétique fournit des informations précieuses sur la réduction du catalyseur, la taille des nanoparticules ferromagnétiques, la chimisorption, ainsi que sur les réactions topo chimiques qui se produisent avec les catalyseurs au cours de la genèse de la phase active et dans des conditions réactionnelles. Les possibilités et les limites de la méthode magnétique sont examinée

Hydrodynamic limits for conservative kinetic equations: a spectral and unified approach in the presence of a spectral gap

Triggered by the fact that, in the hydrodynamic limit, several different kinetic equations of physical interest all lead to the same Navier-Stokes-Fourier system, we develop in the paper an abstract framework which allows to explain this phenomenon. The method we develop can be seen as a significant improvement of known approaches for which we fully exploit some structural assumptions on the linear and nonlinear collision operators as well as a good knowledge of the Cauchy theory for the limiting equation. We adopt a perturbative framework in a Hilbert space setting and first develop a general and fine spectral analysis of the linearized operator and its associated semigroup. Then, we introduce a splitting adapted to the various regimes (kinetic, acoustic, hydrodynamic) present in the kinetic equation which allows, by a fixed point argument, to construct a solution to the kinetic equation and prove the convergence towards suitable solutions to the Navier-Stokes-Fourier system. Our approach is robust enough to treat, in the same formalism, the case of the Boltzmann equation with hard and moderately soft potentials, with and without cut-off assumptions, as well as the Landau equation for hard and moderately soft potentials in presence of a spectral gap. New well-posedness and strong convergence results are obtained within this framework. In particular, for initial data with algebraic decay with respect to the velocity variable, our approach provides the first result concerning the strong Navier-Stokes limit from Boltzmann equation without Grad cut-off assumption or Landau equation. The method developed in the paper is also robust enough to apply, at least at the linear level, to quantum kinetic equations for Fermi-Dirac or Bose-Einstein particles