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We show global-in-time Strichartz estimates for the isotropic Maxwell system with divergence free data. On the scalar permittivity and permeability we impose decay assumptions as $|x|\to\infty$ and a non-trapping condition. The proof is…

Analysis of PDEs · Mathematics 2021-07-01 Piero D'Ancona , Roland Schnaubelt

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…

Analysis of PDEs · Mathematics 2026-02-09 Xiaoqi Huang , Christopher D. Sogge , Zhongkai Tao , Zhexing Zhang

We look for the optimal range of Lebesque exponents for which inhomogeneous Strichartz estimates are valid. We show that it is larger than the one given by admissible exponents for homogeneous estimates. We prove inhomogeneous estimates…

Analysis of PDEs · Mathematics 2007-05-23 Damiano Foschi

We prove spacetime weighted-L^2 estimates for the Schrodinger and wave equation with an inverse-square potential. We then deduce Strichartz estimates for these equations.

Analysis of PDEs · Mathematics 2007-05-23 Nicolas Burq , Fabrice Planchon , John G. Stalker , A. Shadi Tahvildar-Zadeh

We prove some new Strichartz estimates for a class of dispersive equations with radial initial data. In particular, we obtain up to some endpoints the full radial Strichartz estimates for the Schr\"odinger equation. The ideas of proof are…

Analysis of PDEs · Mathematics 2011-05-04 Zihua Guo , Yuzhao Wang

Strichartz estimates are derived from $\ell^2$-decoupling for phase functions satisfying a curvature condition. Bilinear refinements without loss in the high frequency are discussed. Estimates are established from uniform curvature…

Analysis of PDEs · Mathematics 2021-06-15 Robert Schippa

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…

Analysis of PDEs · Mathematics 2023-04-12 Matthew D. Blair , Xiaoqi Huang , Christopher D. Sogge

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

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

We establish new Strichartz estimates for orthonormal families of initial data in the case of the wave, Klein-Gordon and fractional Schr\"odinger equations. Our estimates extend those of Frank-Sabin in the case of the wave and Klein-Gordon…

Analysis of PDEs · Mathematics 2020-04-28 Neal Bez , Sanghyuk Lee , Shohei Nakamura

We prove sharper Strichartz estimates than expected from theoptimal dispersion bounds.

Analysis of PDEs · Mathematics 2016-12-23 Oana Ivanovici , Gilles Lebeau , Fabrice Planchon

Sharp Strichartz estimates are proved for Schr\"odinger and wave equations with Lipschitz coefficients satisfying additional structural assumptions. We use Phillips functional calculus as a substitute for Fourier inversion, which shows how…

Analysis of PDEs · Mathematics 2023-05-16 Dorothee Frey , Robert Schippa

We prove Strichartz estimates with a loss of derivatives for the Schr\"odinger equation on polygonal domains with either Dirichlet or Neumann homogeneous boundary conditions. Using a standard doubling procedure, estimates the on polygon…

Analysis of PDEs · Mathematics 2012-03-05 Matthew D. Blair , G. Austin Ford , Sebastian Herr , Jeremy L. Marzuola

Water waves are well-known to be dispersive at the linearization level. Considering the fully nonlinear systems, we prove for reasonably smooth solutions the optimal Strichartz estimates for pure gravity waves and the semi-classical…

Analysis of PDEs · Mathematics 2016-09-27 Quang-Huy Nguyen

Strong-type inhomogeneous Strichartz estimates are shown to be false for the wave equation outside the so-called acceptable region. On a critical line where the acceptability condition marginally fails, we prove substitute estimates with a…

Classical Analysis and ODEs · Mathematics 2019-02-05 Neal Bez , Jayson Cunanan , Sanghyuk Lee

This paper is concerned with derivation of the global or local in time Strichartz estimates for radially symmetric solutions of the free wave equation from some Morawetz-type estimates via weighted Hardy-Littlewood-Sobolev (HLS)…

Analysis of PDEs · Mathematics 2007-11-14 Kunio Hidano , Yuki Kurokawa

The Strichartz estimates for Schr\"{o}dinger equations can be improved when the data is spread out in either physical or frequency space. In this paper we give refinements of the 2-dimensional homogeneous Strichartz estimate on the maximum…

Classical Analysis and ODEs · Mathematics 2016-12-22 Hong Wang , Lingfu Zhang

We consider the regular Lagrangian flow X associated to a bounded divergence-free vector field b with bounded variation. We prove a Lusin-Lipschitz regularity result for X and we show that the Lipschitz constant grows at most linearly in…

Analysis of PDEs · Mathematics 2021-12-20 Paolo Bonicatto , Elio Marconi

We prove resolvent estimates for a Schr\"odinger operator with a short-range potential outside an obstacle with Dirichlet boundary conditions. As a consequence, we deduce integrability of the local energy for the wave equation, and…

Analysis of PDEs · Mathematics 2024-11-25 Thomas Duyckaerts , Jianwei Urban Yang

We consider the $L_t^2L_x^r$ estimates for the solutions to the wave and Schr\"odinger equations in high dimensions. For the homogeneous estimates, we show $L_t^2L_x^\infty$ estimates fail at the critical regularity in high dimensions by…

Analysis of PDEs · Mathematics 2018-05-04 Zihua Guo , Ji Li , Kenji Nakanishi , Lixin Yan