scholarly journals New counterexamples to Strichartz estimates for the wave equation on a 2D model convex domain

2021 ◽  
Vol 8 ◽  
pp. 1133-1157
Author(s):  
Oana Ivanovici ◽  
Gilles Lebeau ◽  
Fabrice Planchon
Keyword(s):  
Wave Equation ◽  
Convex Domain ◽  
Strichartz Estimates ◽  
2D Model

scholarly journals Strichartz estimates for the wave equation on a 2D model convex domain

2021 ◽  
Vol 300 ◽  
pp. 830-880
Author(s):  
Oana Ivanovici ◽  
Gilles Lebeau ◽  
Fabrice Planchon
Keyword(s):  
Wave Equation ◽  
Convex Domain ◽  
Strichartz Estimates ◽  
2D Model

Strichartz Estimates for Wave Equations with Charge Transfer Hamiltonians

2021 ◽  
Vol 273 (1339) ◽  
Author(s):  
Gong Chen
Keyword(s):  
Wave Equation ◽  
Charge Transfer ◽  
Wave Equations ◽  
Linear Models ◽  
Energy Estimate ◽  
Strichartz Estimates ◽  
Content Type ◽  
Scattering States ◽  
Scattering State ◽  
A Charge

We prove Strichartz estimates (both regular and reversed) for a scattering state to the wave equation with a charge transfer Hamiltonian in R 3 \mathbb {R}^{3} : \[ ∂ t t u − Δ u + ∑ j = 1 m V j ( x − v → j t ) u = 0. \partial _{tt}u-\Delta u+\sum _{j=1}^{m}V_{j}\left (x-\vec {v}_{j}t\right )u=0. \] The energy estimate and the local energy decay of a scattering state are also established. In order to study nonlinear multisoltion systems, we will present the inhomogeneous generalizations of Strichartz estimates and local decay estimates. As an application of our results, we show that scattering states indeed scatter to solutions to the free wave equation. These estimates for this linear models are also of crucial importance for problems related to interactions of potentials and solitons, for example, in [Comm. Math. Phys. 364 (2018), no. 1, pp. 45–82].

A Conjecture Regarding Optimal Strichartz Estimates for the Wave Equation

2017 ◽  
pp. 293-299 ◽  
Author(s):  
Neal Bez ◽  
Chris Jeavons ◽  
Tohru Ozawa ◽  
Hiroki Saito
Keyword(s):  
Wave Equation ◽  
Strichartz Estimates

scholarly journals Strichartz estimates for the Dunkl wave equation and application

2008 ◽  
Vol 346 (1) ◽  
pp. 41-54 ◽  
Author(s):  
Hatem Mejjaoli
Keyword(s):  
Wave Equation ◽  
Strichartz Estimates

scholarly journals Global Strichartz estimates for the wave equation with a time-periodic non-trapping metric

2010 ◽  
Vol 68 (1-2) ◽  
pp. 41-76 ◽  
Author(s):  
Yavar Kian
Keyword(s):  
Wave Equation ◽  
Strichartz Estimates ◽  
Time Periodic

scholarly journals Strichartz estimates and local regularity for the elastic wave equation with singular potentials

2019 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Seongyeon Kim ◽  
◽  
Yehyun Kwon ◽  
Ihyeok Seo ◽  
Keyword(s):  
Wave Equation ◽  
Elastic Wave ◽  
Strichartz Estimates ◽  
Local Regularity ◽  
Singular Potentials ◽  
Elastic Wave Equation
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