Related papers: Sharp $L^4$ Strichartz estimate for Hyperbolic Sch…

We prove the sharp Strichartz estimate for hyperbolic Schr\"{o}dinger equation on $\mathbb{T}^3 $ via an incidence geometry approach. As application, we obtain optimal local well-posedness of nonlinear hyperbolic Schr\"{o}dinger equations.

In this paper, we consider the hyperbolic nonlinear Schr\"odinger equations (HNLS) on $\mathbb{R}\times\mathbb{T}$. We obtain the sharp local well-posedness up to the critical regularity for cubic nonlinearity and in critical spaces for…

We consider the cubic Hyperbolic Schr\"odinger equation \eqref{eq:nls} on torus $\T^2$. We prove that sharp $L^4$ Strichartz estimate, which implies that \eqref{eq:nls} is analytic locally well-posed in in $H^s(\T^2)$ with $s>1/2$,…

We consider the Schr\"odinger equation with no radial assumption on real hyperbolic spaces. We obtain sharp dispersive and Strichartz estimates for a large family of admissible pairs. As a first consequence, we get strong well-posedness…

The optimal $L^4$-Strichartz estimate for the Schr{\"o}dinger equation on the two-dimensional rational torus $\mathbb{T}^2$ is proved, which improves an estimate of Bourgain. A new method based on incidence geometry is used. The approach…

We obtain improved Strichartz estimates for solutions of the Schr\"odinger equation on compact manifolds with nonpositive sectional curvatures which are related to the classical universal results of Burq, G\'erard and Tzvetkov [11]. More…

We obtain improved Strichartz estimates for solutions of the Schr\"odinger equation on negatively curved compact manifolds which improve the classical universal results results of Burq, G\'erard and Tzvetkov [11] in this geometry. In the…

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 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 consider Schr\"odinger equation with a non-degenerate metric on the Euclidean space. We study local in time Strichartz estimates for the Schr\"odinger equation without loss of derivatives including the endpoint case. In contrast to the…

We show the sharp global well posedness for the Cauchy problem for the cubic (quartic) non-elliptic derivative Schr\"odinger equations with small rough data in modulation spaces $M^s_{2,1}(\mathbb{R}^n)$ for $n\ge 3$ ($n= 2$). In 2D cubic…

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…

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…

In this work we consider the Cauchy problem for the cubic Schr\"odinger equation posed on cylinder $\mathbb{R}\times\mathbb{T}$ with fractional derivatives $(-\partial_y^2)^{\alpha},\, \alpha >0$, in the periodic direction. The spatial…

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 Strichartz inequalities for the wave and Schr\"odinger equations on noncompact surfaces with ends of finite area, i.e. with ends isometric to $ \big( (r_0,\infty) \times {\mathbb S}^1 , dr^2 + e^{- 2 \phi (r)}d \theta^2 \big) $…

We prove global weighted Strichartz estimates for radial solutions of linear Schr\"odinger equation on a class of rotationally symmetric noncompact manifolds, generalizing the known results on hyperbolic and Damek-Ricci spaces. This yields…

In the first part of the paper we continue the study of solutions to Schr\"odinger equations with a time singularity in the dispersive relation and in the periodic setting. In the second we show that if the Schr\"odinger operator involves a…

In this paper, we first prove that the cubic, defocusing nonlinear Schr\"odinger equation on the two dimensional hyperbolic space with radial initial data in $H^s(\mathbb{H}^2)$ is globally well-posed and scatters when $s > \frac{3}{4}$.…

Using recent work of Bourgain-Dyatlov we show that for any convex co-compact hyperbolic surface Strichartz estimates for the Schr\"odinger equation hold with an arbitrarily small loss of regularity.