Related papers: On sharp Strichartz estimate for hyperbolic Schr\"…

We prove the sharp $L^4$ Strichartz estimate without derivative loss for the hyperbolic Schr\"odinger equation on $\mathbb{R}\times\mathbb{T}$, \begin{equation} \|e^{it (\partial_{x_{1}}^2-\partial_{x_{2}}^2)}…

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 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.

In this paper, we study the symmetric hyperbolic Schr\"{o}dinger equations in the periodic setting. First, we prove full range Strichartz estimates on general tori by adapting Bourgain's major arc method. The result is sharp for rational…

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 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…

We establish local well-posedness for the hyperbolic nonlinear Schrodinger equation (HNLS) in the critical spaces. Following the approach of Killip and Visan, we derive scale-invariant Strichartz estimates for HNLS on both rational and…

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.

We prove dispersive and Strichartz estimates for Schr\"{o}dinger equations on normal real form symmetric spaces. These estimates apply to the well-posedness and scattering for the nonlinear Schr\"{o}dinger equations.

We prove local in time Strichartz estimates for the Dirac equation on spherically symmetric manifolds. As an application, we give a result of local well-posedness for some nonlinear models.

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…

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 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 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…

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…

In this paper, we prove that the initial value problem for the mass-critical defocusing nonlinear Schr\"odinger equation on the three-dimensional hyperbolic space $\mathbb{H}^3$ is globally well-posed and scatters for data with radial…

We prove a sharp, global-in-time Strichartz estimate for the Schr\"odinger equation on the cylinder $\mathbb{R}\times\mathbb{T}$.

We prove sharp Strichartz-type estimates in three dimensions, including some which hold in reverse spacetime norms, for the wave equation with potential. These results are also tied to maximal operator estimates studied by…

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.…

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 $s > \frac{3}{4}$.…