相关论文: Strichartz estimates for the Schr\"odinger equatio…

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 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…

We prove new lossless Strichartz and spectral projection estimates on asymptotically hyperbolic surfaces, and, in particular, on all convex cocompact hyperbolic surfaces. In order to do this, we also obtain log-scale lossless Strichartz and…

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 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 generalize the Strichartz estimates for Schr\"odinger operators on compact manifolds of Burq, G\'erard and Tzvetkov [10] by allowing critically singular potentials $V$. Specifically, we show that their $1/p$--loss $L^p_tL^q_x(I\times…

We establish Strichartz estimates for the Schr\"odinger equation on Riemannian manifolds $(\Omega,\g)$ with boundary, for both the compact case and the case that $\Omega$ is the exterior of a smooth, non-trapping obstacle in Euclidean…

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 establish new Strichartz estimates for orthonormal systems on compact Riemannian manifolds in the non-sharp admissible region of exponents, covering wave, Klein-Gordon, and fractional Schr\"odinger equations. Our approach combines the…

We prove global-in-time Strichartz estimates without loss of derivatives for the solution of the Schroedinger equation on a class of non-trapping asymptotically conic manifolds. We obtain estimates for the full set of admissible indices,…

We obtain optimal space-time estimates in $L^q_{t,x}$ spaces for all $q\ge 2$ for solutions to the Schr\"odinger equation on Zoll manifolds, including, in particular, the standard round sphere $S^d$. The proof relies on the arithmetic…

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…

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.

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…

We prove global-in-time Strichartz-type estimates for the Schr\"{o}dinger equation on manifolds of the form $\mathbb{R}^{n}\times \mathbb{T}^{d}$, where $\mathbb{T}^{d}$ is a $d$-dimensional torus. Our results generalize and improve a…

We prove two new results about the Cauchy problem for nonlinear Schroedinger equations on four-dimensional compact manifolds. The first one concerns global wellposedness for Hartree-type nonlinearities and includes approximations of cubic…

In this article, we establish scale-invariant Strichartz estimates for the Schr\"odinger equation on arbitrary compact globally symmetric spaces and some bilinear Strichartz estimates on products of rank-one spaces. As applications, we…

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 establish sharp-in-time kernel and dispersive estimates for the Schr\"odinger equation on non-compact Riemannian symmetric spaces of any rank. Due to the particular geometry at infinity and the Kunze-Stein phenomenon, these properties…

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…