The scattering problem for a noncommutative nonlinear Schrödinger equation.
The Schrödinger equation on a compact manifold : Strichartz estimates and applications
We prove Strichartz estimates with fractional loss of derivatives for the Schrödinger equation on any riemannian compact manifold. As a consequence we infer global existence results for the Cauchy problem of nonlinear Schrödinger equations on surfaces in the case of defocusing polynomial nonlinearities, and on three-manifolds in the case of quadratic nonlinearities. We also discuss the optimality of these Strichartz estimates on spheres.
The Schrödinger equation on non-stationary domains.
The Schrödinger–Maxwell system with Dirac mass
The second eigenvalue of the -Laplacian as goes to 1.
The second-order Klein-Gordon field equation.
The Selberg trace formula for the Picard group SL(2, Z[i])
The semiclassical limit of quantum dynamics. II : scattering theory
The semilinear Feng and FMV spectra.
The Semilinear Second-Order Hyperbolic Equation with Data Strongly Singular at One Point.
The shallow water equations: Conservation laws and symplectic geometry.
The shape and smoothness of stable plasma configurations
The shape of the free surface of a unilaterally supported elastic body
The sharp Poincaré inequality for free vector fields: an endpoint result.
The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques
Systems of mixed hyperbolic-elliptic conservation laws can serve as models for the evolution of a liquid-vapor fluid with possible sharp dynamical phase changes. We focus on the equations of ideal hydrodynamics in the isothermal case and introduce a thermodynamically consistent solution of the Riemann problem in one space dimension. This result is the basis for an algorithm of ghost fluid type to solve the sharp-interface model numerically. In particular the approach allows to resolve phase transitions...
The signature package on Witt spaces
In this paper we prove a variety of results about the signature operator on Witt spaces. First, we give a parametrix construction for the signature operator on any compact, oriented, stratified pseudomanifold which satisfies the Witt condition. This construction, which is inductive over the ‘depth’ of the singularity, is then used to show that the signature operator is essentially self-adjoint and has discrete spectrum of finite multiplicity, so that its index—the analytic signature of —is well-defined....
The simple layer potential for the biharmonic equation in variables
A theory of the «simple layer potential» for the classical biharmonic problem in is worked out. This hinges on the study of a new class of singular integral operators, each of them trasforming a vector with scalar components into a vector whose components are differential forms of degree one.
The simplified Wheeler-Dewitt equation : the Cauchy problem and some spectral properties
The Sinc Method in Multiple Space Dimensions: Model Probelms.
The sinc-Galerkin method for solving singularly-perturbed reaction-diffusion problem.