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Related papers: Generalized and weighted Strichartz estimates

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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…

Analysis of PDEs · Mathematics 2023-12-27 Yunfeng Zhang

We prove here essentially sharp linear and bilinear Strichartz type estimates for the wave equations on Minkowski space, where we assume the initial data possesses additional regularity with respect to fractional powers of the usual angular…

Analysis of PDEs · Mathematics 2007-05-23 Jacob Sterbenz , Igor Rodnianski

We introduce new models for Schr\"odinger-type equations, which generalize standard NLS and for which different dispersion occurs depending on the directions. Our purpose is to understand dispersive properties depending on the directions of…

Analysis of PDEs · Mathematics 2023-10-23 Yannick Sire , Xueying Yu , Haitian Yue , Zehua Zhao

We study a well-known problem concerning a random variable $Z$ uniformly distributed between two independent random variables. A new extension has been introduced for this problem and fairly large classes of randomly weighted average…

Statistics Theory · Mathematics 2013-08-27 Hazhir Homei

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…

Mathematical Physics · Physics 2023-12-14 Akitoshi Hoshiya

We prove dispersive and Strichartz estimates for Schr\"o- dinger equations on a class of locally symmetric spaces {\Gamma}\X, where X = G/K is a symmetric space and {\Gamma} is a torsion free discrete sub- group of G. We deal with the cases…

Analysis of PDEs · Mathematics 2015-09-16 Anestis Fotiadis , Nikolaos Mandouvalos , Michel Marias

In this paper we focus on the validity of some fundamental estimates for time-degenerate Schr\"{o}dinger-type operators. On one hand we derive global homogeneous smoothing estimates for operators of any order by means of suitable comparison…

Analysis of PDEs · Mathematics 2024-02-19 Serena Federico , Michael Ruzhansky

We establish Strichartz estimates, including estimates involving spatial derivatives, for radial wave equations with potentials in similarity variables. This is accomplished for all spatial dimensions $d\geq 3$ and almost all regularities…

Analysis of PDEs · Mathematics 2024-11-26 David Wallauch

We obtain the global well-posedness for Schr\"odinger equations of higher orders in weighted $L^2$ spaces. This is based on weighted $L^2$ Strichartz estimates for the corresponding propagator with higher-order dispersion. Our method is…

Analysis of PDEs · Mathematics 2015-03-26 Youngwoo Koh , Ihyeok Seo

We derive a dispersion estimate for one-dimensional perturbed radial Schr\"odinger operators. We also derive several new estimates for solutions of the underlying differential equation and investigate the behavior of the Jost function near…

Spectral Theory · Mathematics 2016-10-13 Aleksey Kostenko , Gerald Teschl , Julio H. Toloza

We study a quite general class of stochastic dispersive equations with linear multiplicative noise, including especially the Schr\"odinger and Airy equations. The pathwise Strichartz and local smoothing estimates are derived here in both…

Probability · Mathematics 2017-09-13 Deng Zhang

The purpose of this paper is to show how local energy decay estimates for certain linear wave equations involving compact perturbations of the standard Laplacian lead to optimal global existence theorems for the corresponding small…

Analysis of PDEs · Mathematics 2013-01-29 Kunio Hidano , Jason Metcalfe , Hart F. Smith , Christopher D. Sogge , Yi Zhou

We prove Strichartz estimates (both regular and reversed) for a scattering state to the wave equation with a charge transfer Hamiltonian in $\mathbb{R}^{3}$: \[ \partial_{tt}u-\Delta u+\sum_{j=1}^{m}V_{j}\left(x-\vec{v}_{j}t\right)u=0. \]…

Analysis of PDEs · Mathematics 2018-09-05 Gong Chen

In this paper we continue the analysis of the dispersive properties of the 2D and 3D massless Dirac-Coulomb equations that has been started in arXiv:1503.00945 and arXiv:2101.07185. We prove a priori estimates of the solution of the…

Analysis of PDEs · Mathematics 2024-10-16 Elena Danesi

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…

Analysis of PDEs · Mathematics 2017-08-08 Kouichi Taira

This paper is devoted to study the dispersive properties of the linear Klein-Gordon and wave equations on a class of locally symmetric spaces. As a consequence, we obtain the Strichartz estimate and prove global well-posedness results for…

Analysis of PDEs · Mathematics 2019-08-27 Hong-Wei Zhang

We show trilinear Strichartz estimates in one and two dimensions on frequency-dependent time intervals. These improve on the corresponding linear estimates of periodic solutions to the Schr\"odinger equation. The proof combines decoupling…

Analysis of PDEs · Mathematics 2023-12-12 Robert Schippa

In this paper we study the Strichartz estimates for the Schr\"odinger propagator in the context of Wiener amalgam spaces which, unlike the Lebesgue spaces, control the local regularity of a function and its decay at infinity separately.…

Analysis of PDEs · Mathematics 2019-05-20 Seongyeon Kim , Youngwoo Koh , Ihyeok Seo

In this paper, we show that certain local Strichartz estimates for solutions of the wave equation exterior to a convex obstacle can be extended to estimates that are global in both space and time. This extends the work that was done…

Analysis of PDEs · Mathematics 2007-05-23 Jason Metcalfe

We consider Strichartz estimates for the wave equation with respect to general measures which satisfy certain growth condition. In $\mathbb R^{3+1}$ we obtain the sharp estimate and in higher dimensions improve the previous results.

Analysis of PDEs · Mathematics 2016-12-22 Chu-Hee Cho , Seheon Ham , Sanghyuk Lee