A representation formula for the voltage perturbations caused by diametrically small conductivity inhomogeneities. Proof of uniform validity
A result of existence for an original convection-diffusion equation.
En este artículo se estudia el análisis matemático de una ley de conservación que no es clásica. El modelo describe procesos estatigráficos en Geología y tiene en cuenta una condición de tasa de erosión limitada. En primer lugar se presentan el modelo físico y la formulación matemática (posiblemente nueva). Tras enunciar la definición solución se presentan las herramientas que permiten probar la existencia de soluciones.
A review on the improved regularity for the primitive equations
In this work we will study some types of regularity properties of solutions for the geophysical model of hydrostatic Navier-Stokes equations, the so-called Primitive Equations (PE). Also, we will present some results about uniqueness and asymptotic behavior in time.
A Riemann–Hilbert problem and the Bernoulli boundary condition in the variational theory of Stokes waves
A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators
We study the homogeneous Riemann-Hilbert problem with a vanishing scalar-valued continuous coefficient. We characterize non-existence of nontrivial solutions in the case where the coefficient has its values along several rays starting from the origin. As a consequence, some results on injectivity and existence of eigenvalues of Toeplitz operators in Hardy spaces are obtained.
A rigorous derivation of free-boundary problem arising in superconductivity
A second-order multi-fluid model for evaporating sprays
The aim of this paper is to present a method using both the ideas of sectional approach and moment methods in order to accurately simulate evaporation phenomena in gas-droplets flows. Using the underlying kinetic interpretation of the sectional method [Y. Tambour, Combust. Flame 60 (1985) 15–28] exposed in [F. Laurent and M. Massot, Combust. Theory Model. 5 (2001) 537–572], we propose an extension of this approach based on a more accurate representation of the droplet size number density in each...
A second-order multi-fluid model for evaporating sprays
The aim of this paper is to present a method using both the ideas of sectional approach and moment methods in order to accurately simulate evaporation phenomena in gas-droplets flows. Using the underlying kinetic interpretation of the sectional method [Y. Tambour, Combust. Flame60 (1985) 15–28] exposed in [F. Laurent and M. Massot, Combust. Theory Model.5 (2001) 537–572], we propose an extension of this approach based on a more accurate representation of the droplet size number density in each...
A semi-classical picture of quantum scattering
A shape optimization approach for a class of free boundary problems of Bernoulli type
We are interested in an optimal shape design formulation for a class of free boundary problems of Bernoulli type. We show the existence of the optimal solution of this problem by proving continuity of the solution of the state problem with respect to the domain. The main tools in establishing such a continuity are a result concerning uniform continuity of the trace operator with respect to the domain and a recent result on the uniform Poincaré inequality for variable domains.
A short note on theory for Stokes problem with a pressure-dependent viscosity
We study higher local integrability of a weak solution to the steady Stokes problem. We consider the case of a pressure- and shear-rate-dependent viscosity, i.e., the elliptic part of the Stokes problem is assumed to be nonlinear and it depends on and on the symmetric part of a gradient of , namely, it is represented by a stress tensor which satisfies -growth condition with . In order to get the main result, we use Calderón-Zygmund theory and the method which was presented for example in...
A short note on regularity criteria for the Navier-Stokes equations containing the velocity gradient
We review several regularity criteria for the Navier-Stokes equations and prove some new ones, containing different components of the velocity gradient.
A singular perturbation problem in a system of nonlinear Schrödinger equation occurring in Langmuir turbulence
A singular perturbation problem in a system of nonlinear Schrödinger equation occurring in Langmuir turbulence
The aim of this work is to establish, from a mathematical point of view, the limit α → +∞ in the system where . This corresponds to an approximation which is made in the context of Langmuir turbulence in plasma Physics. The L2-subcritical σ (that is σ ≤ 2/3) and the H1-subcritical σ (that is σ ≤ 2) are studied. In the physical case σ = 1, the limit is then studied for the norm.
A singular perturbation problem in exact controllability of the Maxwell system
This paper studies the exact controllability of the Maxwell system in a bounded domain, controlled by a current flowing tangentially in the boundary of the region, as well as the exact controllability the same problem but perturbed by a dissipative term multiplied by a small parameter in the boundary condition. This boundary perturbation improves the regularity of the problem and is therefore a singular perturbation of the original problem. The purpose of the paper is to examine the connection,...
A Singular Perturbation Problem in Exact Controllability of the Maxwell System
This paper studies the exact controllability of the Maxwell system in a bounded domain, controlled by a current flowing tangentially in the boundary of the region, as well as the exact controllability the same problem but perturbed by a dissipative term multiplied by a small parameter in the boundary condition. This boundary perturbation improves the regularity of the problem and is therefore a singular perturbation of the original problem. The purpose of the paper is to examine the connection, for...
A Slideing Mesh-Mortar Method for a two Dimensional Currents Model of Electric Engines
The paper deals with the application of a non-conforming domain decomposition method to the problem of the computation of induced currents in electric engines with moving conductors. The eddy currents model is considered as a quasi-static approximation of Maxwell equations and we study its two-dimensional formulation with either the modified magnetic vector potential or the magnetic field as primary variable. Two discretizations are proposed, the first one based on curved finite elements and the...
A sliding Mesh-Mortar method for a two dimensional Eddy currents model of electric engines
The paper deals with the application of a non-conforming domain decomposition method to the problem of the computation of induced currents in electric engines with moving conductors. The eddy currents model is considered as a quasi-static approximation of Maxwell equations and we study its two-dimensional formulation with either the modified magnetic vector potential or the magnetic field as primary variable. Two discretizations are proposed, the first one based on curved finite elements and the...
A smoothing property for the -critical NLS equations and an application to blowup theory
A spatially periodic Kuramoto-Sivashinsky equation as a model problem for inclined film flow over wavy bottom.