Related papers: Strichartz estimates for Schr\"odinger equations w…

We prove that the stationary magnetic potential vector and the electrostatic potential entering the dynamic magnetic Schr\"odinger equation can be Lipschitz stably retrieved through finitely many local boundary measurements of the solution.…

We consider magnetic Schr\"odinger equations with sublinear magnetic potentials and subquadratic electric potentials on $\mathbb{R}^{d}$, as well as generalizations thereof. We obtain new results on the global well-posedness of the Cauchy…

In this paper, we investigate Strichartz estimates for discrete linear Schr\"odinger and discrete linear Klein-Gordon equations on a lattice $h\mathbb{Z}^d$ with $h>0$, where $h$ is the distance between two adjacent lattice points. As for…

We consider an $n$-dimensional spherically symmetric, asymptotically Euclidean manifold with two ends and a codimension 1 trapped set which is degenerately hyperbolic. By separating variables and constructing a semiclassical parametrix for…

We study linear Klein-Gordon equations with moving potentials motivated by the stability analysis of traveling waves and multi-solitons. In this paper, Strichartz estimates, local energy decay and the scattering theory for these models are…

In this note we consider the Schr\"odinger equation on compact manifolds equipped with possibly degenerate metrics. We prove Strichartz estimates with a loss of derivatives. The rate of loss of derivatives depends on the degeneracy of…

We prove global Strichartz inequalities for the Schr\"odinger equation on a large class of asymptotically conical manifolds. Letting $ P $ be the nonnegative Laplace operator and $ f_0 \in C_0^{\infty}({\mathbb R}) $ be a smooth cutoff…

Strichartz estimates for a time-decaying harmonic oscillator were proven with some assumptions of coefficients for the time-decaying harmonic potentials. The main results of this paper are to remove these assumptions and to enable us to…

In this paper, we study Strichartz estimates for the Schr\"odinger equation on a metric cone $X$, where $X=C(Y)=(0,\infty)_r\times Y$ and the cross section $Y$ is a $(n-1)$-dimensional closed Riemannian manifold $(Y,h)$. For the metric $g$…

In this paper we study Strichartz estimates for the half wave, the half Klein-Gordon and the Dirac Equations on compact manifolds without boundary, proving in particular for each of these flows local in time estimates both for the wave and…

The purpose of this paper is to study the validity of global-in-time Strichartz estimates for the Schr\"odinger equation on $\mathbb{R}^n$, $n\ge3$, with the negative inverse-square potential $-\sigma|x|^{-2}$ in the critical case…

We prove Strichartz estimates for the Schroedinger operator $H = -\Delta + V(t,x)$ with time-periodic complex potentials $V$ belonging to the scaling-critical space $L^{n/2}_x L^\infty_t$ in dimensions $n \ge 3$. This is done directly from…

We prove almost Strichartz estimates found after adding regularity in the spherical coordinates for Schr\"odinger-like equations. The estimates are sharp up to endpoints. The proof relies on estimates involving spherical averages. Sharpness…

The purpose in this paper is to prove end point Strichartz estimates for the Schr\"odinger equation in the exterior domain of a generic non-trapping obstacle in the case $n \geq 3.$ In the case $n=2$ we have the same range of Strichartz…

We investigate dispersive and Strichartz estimates for the Schr\"odinger equation involving the fractional Laplacian in real hyperbolic spaces and their discrete analogues, homogeneous trees. Due to the Knapp phenomenon, the Strichartz…

In this paper we prove sharp resolvent estimates for the magnetic Schr\"odinger operator in $\mathbb{R}^d$, $d\ge 3$, with $L^\infty$ short-range electric and magnetic potentials. We also show that these resolvent estimates still hold for…

The purpose of this article is to construct global solutions, in a probabilistic sense, for the nonlinear Schr{\"o}dinger equation posed on $\mathbb{R}^d$, in a supercritical regime. Firstly, we establish Bourgain type bilinear estimates…

In this paper we consider magnetic Schr\"odinger operators in R^n, n \ge 3. Under almost optimal conditions on the potentials in terms of decay and regularity we prove smoothing and Strichartz estimates, as well as a limiting absorption…

We study a non-linear Schroedinger equation with a Hartree-type nonlinearity and a localized random time-dependent external potential. Sharp dispersive estimates for the linear Schroedinger equation with a random time-dependent potential…

We prove Strichartz estimates without loss for the Schr\"odinger equation and the wave equation outside finitely many strictly convex obstacles verifying Ikawa's condition, extending the approach we introduced previously for the two convex…