Hyperbolic methods for Einstein's equations.
Hypergeometric solutions of the quantum differential equation of the cotangent bundle of a partial flag variety
We describe hypergeometric solutions of the quantum differential equation of the cotangent bundle of a partial flag variety. These hypergeometric solutions manifest the Landau-Ginzburg mirror symmetry for the cotangent bundle of a partial flag variety.
Il criterio dell'energia e Vequazione di Maxwell-Cattaneo nella termodinamica dei sistemi elettromagnetici non lineari
We study the evolution law of the canonical energy of an electromagnetic material, immersed in an environment that is thermally and electromagnetically passive, at constant temperature. We use as constitutive equation for the heat flux a Maxwell-Cattaneo like equation.
Il paradosso elettrotermico
Ill-posed Cauchy problems for ideal gas equations and their regularization
Ill-posedness for the Navier-Stokes and Euler equations in Besov spaces
We construct a new initial data to prove the ill-posedness of both Navier-Stokes and Euler equations in weaker Besov spaces in the sense that the solution maps to these equations starting from are discontinuous at .
Impact of the variations of the mixing length in a first order turbulent closure system
This paper is devoted to the study of a turbulent circulation model. Equations are derived from the “Navier-Stokes turbulent kinetic energy” system. Some simplifications are performed but attention is focused on non linearities linked to turbulent eddy viscosity . The mixing length acts as a parameter which controls the turbulent part in . The main theoretical results that we have obtained concern the uniqueness of the solution for bounded eddy viscosities and small values of and its asymptotic...
Impact of the variations of the mixing length in a first order turbulent closure system
This paper is devoted to the study of a turbulent circulation model. Equations are derived from the “Navier-Stokes turbulent kinetic energy” system. Some simplifications are performed but attention is focused on non linearities linked to turbulent eddy viscosity . The mixing length acts as a parameter which controls the turbulent part in . The main theoretical results that we have obtained concern the uniqueness of the solution for bounded eddy viscosities and small values of and its asymptotic...
Implicit difference scheme for the numerical resolution of the Charney-Obukhov equation with variable coefficients.
Improved estimates for the Ginzburg-Landau equation : the elliptic case
We derive estimates for various quantities which are of interest in the analysis of the Ginzburg-Landau equation, and which we bound in terms of the -energy and the parameter . These estimates are local in nature, and in particular independent of any boundary condition. Most of them improve and extend earlier results on the subject.
Improved successive constraint method based a posteriori error estimate for reduced basis approximation of 2D Maxwell's problem
In a posteriori error analysis of reduced basis approximations to affinely parametrized partial differential equations, the construction of lower bounds for the coercivity and inf-sup stability constants is essential. In [Huynh et al., C. R. Acad. Sci. Paris Ser. I Math.345 (2007) 473–478], the authors presented an efficient method, compatible with an off-line/on-line strategy, where the on-line computation is reduced to minimizing a linear functional under a few linear constraints. These constraints...
Improving Cancer Therapy by Doxorubicin and Granulocyte Colony-Stimulating Factor: Insights from a Computerized Model of Human Granulopoiesis
Neutropenia is a significant dose-limiting toxicity of cancer chemotherapy, especially in dose-intensified regimens. It is widely treated by injections of Granulocyte Colony-Stimulating Factor (G-CSF). However, optimal schedules of G-CSF administration are still not determined. In order to aid in identifying more efficacious and less neutropenic treatment protocols, we studied a detailed physiologically-based computer model of granulopoiesis, as affected by different treatment schedules of doxorubicin...
Impuretés dans une structure périodique
Incompressible flows of an ideal fluid with vorticity in borderline spaces of Besov type
Incompressible inviscid limit for the full magnetohydrodynamic flows on expanding domains
In this paper we study the incompressible inviscid limit of the full magnetohydrodynamic flows on expanding domains with general initial data. By applying the relative energy method and carrying out detailed analysis on the oscillation part of the velocity, we prove rigorously that the gradient part of the weak solutions of the full magnetohydrodynamic flows converges to the strong solution of the incompressible Euler system in the whole space, as the Mach number, viscosity as well as the heat conductivity...
Incompressible, inviscid limit of the compressible Navier–Stokes system
Incompressible limit of a fluid-particle interaction model
The incompressible limit of the weak solutions to a fluid-particle interaction model is studied in this paper. By using the relative entropy method and refined energy analysis, we show that, for well-prepared initial data, the weak solutions of the compressible fluid-particle interaction model converge to the strong solution of the incompressible Navier-Stokes equations as long as the Mach number goes to zero. Furthermore, the desired convergence rates are also obtained.
Incompressible Maxwell-Boussinesq approximation: Existence, uniqueness and shape sensitivity
Induced trajectories and approximate inertial manifolds
Inégalités de Carleman globales pour les problèmes elliptiques non homogènes
On établit ici, suivant [5], une inégalité de Carleman globale optimale pour les solutions faibles (au sens ) d’équations elliptiques générales avec second membre dans et trace non nulle.La motivation, qui est expliquée dans l’introduction, réside dans l’obtention d’inégalités de Carleman globale pour l’opérateur de Navier-Stokes linéarisé afin, notamment, d’étudier les questions de contrôlabilité exacte sur les trajectoires pour les équations de Navier-Stokes. Une étape majeure consiste à obtenir...