Related papers: Semiclassical limit of orthonormal Strichartz esti…

We study the global-in-time Strichartz estimates for the Schr\"odinger equation on a class of scattering manifolds $X^{\circ}$. Let $\mathcal{L}_V=\Delta_g+V$ where $\Delta_g$ is the Beltrami-Laplace operator on the scattering manifold and…

We prove sharp Strichartz estimates for the semi-classical Schrodinger equation on a compact manifold with smooth, strictly geodesically concave boundary. We deduce sharp (classical) Strichartz estimates for the Schrodinger equation outside…

The present paper is concerned with Schr\"odinger equations with variable coefficients and unbounded electromagnetic potentials, where the kinetic energy part is a long-range perturbation of the flat Laplacian and the electric (resp.…

We prove local in time Strichartz estimates without loss for the restriction of the solution of the Schroedinger equation, outside a large compact set, on a class of asymptotically hyperbolic manifolds.

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…

In this article we study global-in-time Strichartz estimates for the Schr\"odinger evolution corresponding to long-range perturbations of the Euclidean Laplacian. This is a natural continuation of a recent article of the third author, where…

In this paper we prove local-in-time Strichartz estimates with loss of derivatives for Schr\"odinger equations with variable coefficients and potentials, under the conditions that the geodesic flow is nontrapping and potentials grow…

In this paper we introduce a notion of scattering theory for the Laplace-Beltrami operator on non-compact, connected and complete Riemannian manifolds. A principal condition is given by a certain positive lower bound of the second…

We establish new Strichartz estimates for orthonormal systems on compact Riemannian manifolds in the case of wave, Klein-Gordon and fractional Schr\"odinger equations. Our results generalize the classical (single-function) Strichartz…

We prove global Strichartz estimates (with spectral cutoff on the low frequencies) for non trapping metric perturbations of the Schroedinger equation, posed on the Euclidean space.

In this paper, we prove global in time Strichartz estimates for the fractional Schr\"odinger operators, namely $e^{-it\Lambda_g^\sigma}$ with $\sigma \in (0,\infty)\backslash \{1\}$ and $\Lambda_g:=\sqrt{-\Delta_g}$ where $\Delta_g$ is the…

In this short paper, we prove Strichartz estimates for N-body Schr\"odinger equations in the waveguide manifold setting (i.e. on semiperiodic spaces $\mathbb{R}^m\times \mathbb{T}^n$ where $m\geq 3$), provided that interaction potentials…

We prove local Strichartz estimates on compact manifolds with boundary. Our results also apply more generally to compact manifolds with Lipschitz metrics.

We develop an abstract perturbation theory for the orthonormal Strichartz estimates, which were first studied by Frank-Lewin-Lieb-Seiringer. The method used in the proof is based on the duality principle and the smooth perturbation theory…

In this paper we prove some new Strichartz estimates related to the Cauchy problem for the Bessel operator on the half-line and we establish a fractal version of the Tomas-Stein restriction theorem for the Hankel transform. Then we use the…

Doi proved that the $L^2_t H^{1/2}_x$ local smoothing effect for Schr\"odinger equation on a Riemannian manifold does not hold if the geodesic flow has one trapped trajectory. We show in contrast that Strichartz estimates and $L^1\to…

We study the nonlinear Klein-Gordon equation on a product space $M=\R\times X$ with metric $\tilde{g}=dt^2-g$ where $g$ is the scattering metic on $X$. We establish the global-in-time Strichartz estimate for Klein-Gordon equation without…

We prove resolvent estimates for semiclassical operators such as $-h^2 \Delta+V(x)$ in scattering situations. Provided the set of trapped classical trajectories supports a chaotic flow and is sufficiently filamentary, the analytic…

We prove a resolvent estimate for the Laplace-Beltrami operator on a scattering manifold with a hyperbolic trapped set, and as a corollary deduce local smoothing. We use a result of Nonnenmacher-Zworski to provide an estimate near the…

We obtain the Strichartz inequalities $$ \| u \|_{L^q_t L^r_x([0,1] \times M)} \leq C \| u(0) \|_{L^2(M)}$$ for any smooth $n$-dimensional Riemannian manifold $M$ which is asymptotically conic at infinity (with either short-range or…