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We study the dispersive behaviors of two-particles Schr\"odinger and wave equations in the Aharonov-Bohm field. In particular, we prove the Strichartz estimates for Schr\"odinger and wave equations in this setting. The key point is to…

Analysis of PDEs · Mathematics 2021-10-14 Xiaofen Gao , Junyong Zhang , Jiqiang Zheng

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…

Analysis of PDEs · Mathematics 2014-06-24 Haruya Mizutani

The work treats smoothing and dispersive properties of solutions to the Schrodinger equation with magnetic potential. Under suitable smallness assumption on the potential involving scale invariant norms we prove smoothing - Strichartz…

Algebraic Topology · Mathematics 2010-08-25 Vladimir Georgiev , Atanas Stefanov , Mirko Tarulli

In this paper, we explore the relations between different kinds of Strichartz estimates and give new estimates in Euclidean space $\mathbb{R}^n$. In particular, we prove the generalized and weighted Strichartz estimates for a large class of…

Analysis of PDEs · Mathematics 2012-07-24 Jin-Cheng Jiang , Chengbo Wang , Xin Yu

This paper proves Strichartz estimates for the Schrodinger Equation with a potential term and white noise dispersion in dimension $1$. We also explore dispersive estimates using previous results in the field.

Analysis of PDEs · Mathematics 2024-10-08 Abhinav Goel

Let $H$ be a selfadjoint operator and $A$ a closed operator on a Hilbert space $\mathcal{H}$. If $A$ is $H$-(super)smooth in the sense of Kato-Yajima, we prove that $AH^{-\frac14}$ is $\sqrt{H}$-(super)smooth. This allows to include wave…

Analysis of PDEs · Mathematics 2019-07-25 Piero D'Ancona

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 prove Strichartz estimates for the Schr\"odinger equation with scaling-critical electromagnetic potentials in dimensions $n\geq3$. The decay assumption on the magnetic potentials is critical, including the case of the Coulomb potential.…

Analysis of PDEs · Mathematics 2025-05-20 Qiuye Jia , Junyong Zhang

In this paper we study the linear and nonlinear Schr\"odinger equations associated with the Ornstein-Uhlenbeck (OU) operator endowed with the Gaussian measure. While classical Strichartz estimates are well-developed for the free…

Functional Analysis · Mathematics 2025-07-08 Aparajita Dasgupta , Uttam Kumar Dolai , Cheng Luo , Manli Song

We obtain weighted $L^2$ Strichartz estimates for Schr\"odinger equations $i\partial_tu+(-\Delta)^{a/2}u=F(x,t)$, $u(x,0)=f(x)$, of general orders $a>1$ with radial data $f,F$ with respect to the spatial variable $x$, whenever the weight is…

Analysis of PDEs · Mathematics 2017-05-11 Youngwoo Koh , Ihyeok Seo

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…

Analysis of PDEs · Mathematics 2016-08-31 Marius Beceanu , Michael Goldberg

We prove local smoothing and weighted Strichartz estimates for the Dirac equation with a Aharonov-Bohm potential. The proof relies on an explicit representation of the solution built in terms of spectral projections.

Analysis of PDEs · Mathematics 2017-01-02 Federico Cacciafesta , Luca Fanelli

We establish dispersive and Strichartz estimates for solutions to the linear time-dependent Schr\"odinger equations with potential in three dimensions. Our main focus is on the small rough time-dependent potentials. Examples of such…

Analysis of PDEs · Mathematics 2007-05-23 I. Rodnianski , W. Schlag

We present abstract inhomogeneous Strichartz estimates for dispersive operators, extending previous work by M. Keel and T. Tao on the one hand, and generalising results of D. Foschi, M. Vilela, M. Nakamura and T. Ozawa on the other hand. It…

Analysis of PDEs · Mathematics 2008-02-29 Robert J Taggart

In this paper, we investigate Strichartz estimates for discrete linear Schr\"odinger and discrete linear Klein-Gordon equations on a lattice $h\mathbb{Z}^d$ with $h>0$, where $h$ is the distance between two adjacent lattice points. As for…

Analysis of PDEs · Mathematics 2018-06-20 Younghun Hong , Changhun Yang

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 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…

Analysis of PDEs · Mathematics 2007-08-19 Valeria Banica , Thomas Duyckaerts

There have been a lot of works concerning the Strichartz estimates for the perturbed Schr\"odinger equation by potential. These can be basically carried out adopting the well-known procedure for obtaining the Strichartz estimates from the…

Analysis of PDEs · Mathematics 2021-02-24 Seongyeon Kim , Ihyeok Seo , Jihyeon Seok

We study a quantum and classical correspondence related to the Strichartz estimates. First we consider the orthonormal Strichartz estimates on manifolds with ends. Under the nontrapping condition we prove the global-in-time estimates on…

Analysis of PDEs · Mathematics 2025-11-26 Akitoshi Hoshiya

The aim of the paper is twofold. We establish refined Strichartz estimates for the Schr\"odinger equation on tori within the framework of partial regularity. As a result, we reveal that the solution of the free Schr\"odinger equation has…

Analysis of PDEs · Mathematics 2026-01-29 Divyang G. Bhimani , Subhash. R. Choudhary , S. S. Mondal