Related papers: Smoothing estimates for variable coefficients Schr…

We prove a local in time smoothing estimate for a magnetic Schrodinger equation with coefficients growing polynomially at spatial infinity. The assumptions on the magnetic field are gauge invariant and involve only the first two…

The work treats smoothing and dispersive properties of solutions to the Schrodinger equation with magnetic potential. Under suitable smallness assumption on the potential involving scale invariant norms we prove smoothing - Strichartz…

We prove smoothing estimates for Schr\"odinger equations $i\partial_t \phi+\partial_x (a(x) \partial_x \phi) =0$ with $a(x)\in \mathrm{BV}$, the space of functions with bounded total variation, real, positive and bounded from below. We then…

The smoothing effect states that solutions to the Schr{\"o}dinger equation in the Euclidean space have, for almost-every time, a local-in-space improved regularity (gain of half a derivative in Sobolev spaces). In this note, we show that,…

This paper mainly addresses the strong unique continuation property for the electromagnetic Schr\"{o}dinger operator with complex-valued coefficients. Appropriate multipliers with physical backgrounds have been introduced to prove a priori…

We prove a family of identities that involve the solutions to the free Schreodinger equation. As a consequence of these identities we shall deduce a lower bound for the local smoothing estimate and a uniqueness criterion.

We prove global smoothing and Strichartz estimates for the Schroedinger, wave, Klein-Gordon equations and for the massless and massive Dirac systems, perturbed with singular electromagnetic potentials. We impose a smallness condition on the…

We study local and global existence and smoothing properties for the initial value problem associated to a higher order nonlinear Schr\"odinger equation with constant coefficients which appears as a model for propagation of pulse in optical…

We are mainly interested in extending the known results on ob-servability inequalities and stabilization for the Schr{\"o}dinger equation to the magnetic Schr{\"o}dinger equation. That is in presence of a magnetic potential. We establish…

Exponential smoothers are a simple and memory efficient way to compute running averages of time series. Here we define and describe practical properties of exponential smoothers for signals observed at constant and variable intervals.

In this expository note, we prove some extensions and refinements of classical Kato type estimates with elementary techniques.

We prove sharp local smoothing estimates for wave equations on compact Riemannian manifolds in $n+1$ dimensions for odd $n$ and obtain improved estimates in even dimensions. This is achieved by deriving local smoothing estimates for certain…

We extend the conforming virtual element method to the numerical resolution of eigenvalue problems with potential terms on a polytopal mesh. An important application is that of the Schrodinger equation with a pseudopotential term. This…

We formulate a smoothed-particle hydrodynamics numerical method, traditionally used for the Euler equations for fluid dynamics in the context of astrophysical simulations, to solve the non-linear Schrodinger equation in the Madelung…

In this paper we prove the smoothing effect for solutions of Schr{\"o}dinger equations with variable coefficients and in a non trapping exterior domain. We allow quadratic potentials at infinity.

We give a pedagogical introduction of the stochastic variational method by considering the quantization of a non-inertial particle system. We show that the effects of fictitious forces are represented in the forms of vector fields which…

This paper applies Hermite function techniques to give elementary proofs of Kato type smoothing estimates for the Schr\"odinger equation with quadratic potential in R^n+1. This is equivalent to proving a uniform L^2(R^n) to L^2(R^n)…

We consider some scale invariant generalizations of the smoothing estimates for the free Schr\"odnger equation obtained by Kenig, Ponce and Vega. Applying these estimates and using appropriate commutator estimates, we obtain similar scale…

We prove a variable coefficient version of the square function estimate of Guth--Wang--Zhang. By a classical argument of Mockenhaupt--Seeger--Sogge, it implies the full range of sharp local smoothing estimates for $2+1$ dimensional Fourier…

In this paper, we establish a boundary observability estimate for stochastic Schr\"{o}dinger equations by means of the global Carleman estimate. Our Carleman estimate is based on a new fundamental identity for a stochastic…