Eine Außenraumaufgabe für die instationären Navier-Stokes-Gleichungen.
Einstein-Euler equations for matter spacetimes with Gowdy symmetry
We investigate the initial value problem for the Einstein-Euler equations of general relativity under the assumption of Gowdy symmetry on . Given an arbitrary initial data set, we establish the existence of a globally hyperbolic future development and we provide a global foliation of this spacetime in terms of a geometrically defined time-function coinciding with the area of the orbits of the symmetry group. This allows us to construct matter spacetimes with weak regularity which admit, both, impulsive...
Ekman boundary layers in rotating fluids
In this paper, we investigate the problem of fast rotating fluids between two infinite plates with Dirichlet boundary conditions and “turbulent viscosity” for general initial data. We use dispersive effect to prove strong convergence to the solution of the bimensionnal Navier-Stokes equations modified by the Ekman pumping term.
Ekman boundary layers in rotating fluids
In this paper, we investigate the problem of fast rotating fluids between two infinite plates with Dirichlet boundary conditions and “turbulent viscosity” for general L2 initial data. We use dispersive effect to prove strong convergence to the solution of the bimensionnal Navier-Stokes equations modified by the Ekman pumping term.
Electromagnetic fields in linear and nonlinear chiral media: a time-domain analysis.
Electromagnetic scattering at composite objects : a novel multi-trace boundary integral formulation
Since matrix compression has paved the way for discretizing the boundary integral equation formulations of electromagnetics scattering on very fine meshes, preconditioners for the resulting linear systems have become key to efficient simulations. Operator preconditioning based on Calderón identities has proved to be a powerful device for devising preconditioners. However, this is not possible for the usual first-kind boundary formulations for electromagnetic...
Electromagnetic scattering at composite objects : a novel multi-trace boundary integral formulation
Since matrix compression has paved the way for discretizing the boundary integral equation formulations of electromagnetics scattering on very fine meshes, preconditioners for the resulting linear systems have become key to efficient simulations. Operator preconditioning based on Calderón identities has proved to be a powerful device for devising preconditioners. However, this is not possible for the usual first-kind boundary formulations for electromagnetic...
Electroosmotic pumping in rectangular microchannels: a numerical treatment by the finite element method.
Elementary linear algebra for advanced spectral problems
We describe a simple linear algebra idea which has been used in different branches of mathematics such as bifurcation theory, partial differential equations and numerical analysis. Under the name of the Schur complement method it is one of the standard tools of applied linear algebra. In PDE and spectral analysis it is sometimes called the Grushin problem method, and here we concentrate on its uses in the study of infinite dimensional problems, coming from partial differential operators of mathematical...
Elements of a qualitative theory of Hamiltonian PDEs.
Elliptic quasi-variational inequalities and application to a non-stationary problem in hydraulics
Elliptic regularization and Navier-Stokes system.
Energy concentration for the Landau–Lifshitz equation
Energy Critical nonlinear Schrödinger equations in the presence of periodic geodesics
This is a report on recent progress concerning the global well-posedness problem for energy-critical nonlinear Schrödinger equations posed on specific Riemannian manifolds with small initial data in . The results include small data GWP for the quintic NLS in the case of the flat rational torus and small data GWP for the corresponding cubic NLS in the cases and . The main ingredients are bi-linear and tri-linear refinements of Strichartz estimates which obey the critical scaling, as well...
Energy Functionals in Scattering Theory
Enthalpy model for heating, melting, and vaporization in laser ablation.
Entropy compactification of the transonic flow
Entropy solutions to the Buckley--Leverett equations.
Envelopes of holomorphy for solutions of the Laplace and Dirac equations
Analytic continuation and domains of holomorphy for solution to the complex Laplace and Dirac equations in are studied. First, geometric description of envelopes of holomorphy over domains in is given. In more general case, solutions can be continued by integral formulas using values on a real dimensional cycle in . Sufficient conditions for this being possible are formulated.
Équation anisotrope de Navier-Stokes dans des espaces critiques.
We study the tridimensional Navier-Stokes equation when the value of the vertical viscosity is zero, in a critical space (invariant by the scaling). We shall prove local in time existence of the solution, respectively global in time when the initial data is small compared with the horizontal viscosity.