Decay and Strichartz estimates in critical electromagnetic fields

Gao, Xiaofen; Yin, Zhiqing; Zhang, Junyong; Zheng, Jiqiang

doi:10.1016/j.jfa.2021.109350

Cited by 10 publications

(6 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Now, the proof of (5.10) is very similar to the one of the corresponding estimate for the half-wave propagator as developed in [36,37]; we include a proof in the appendix for the sake of completeness. Finally, recalling (5.9), and thanks to the fact that φ = 1 on the support of ϕ, we see that (1.21) is an immediate consequence of (5.10).…”

Section: Construction Of the Dirac Propagatormentioning

confidence: 72%

See 1 more Smart Citation

Generalized Strichartz estimates for wave and Dirac equations in Aharonov–Bohm magnetic fields

Cacciafesta

Yin

Zhang

2022

Dynamics of Partial Differential Equations

View full text Add to dashboard Cite

In this paper we study the dispersive properties of a two dimensional massless Dirac equation perturbed by an Aharonov-Bohm magnetic field. Our main results will be a family of pointwise decay estimates and a full range family Strichartz estimates for the flow. The proof relies on the use of a relativistic Hankel transform, which allows for an explicit representation of the propagator in terms of the generalized eigenfunctions of the operator. These results represent the natural continuation of earlier research on evolution equations associated to operators with magnetic fields with strong singularities (see [21,35,36] where the Schrödinger and the wave equations were studied). Indeed, we recall the fact that the Aharonov-Bohm field represents a perturbation which is critical with respect to the scaling: this fact, as it is well known, makes the analysis particularly challenging.

show abstract

Section: Construction Of the Dirac Propagatormentioning

confidence: 72%

“…Very recently, Fanelli, Zheng and the last author [36] established Strichartz estimates for the wave equation in 2D by constructing the odd sin propagator. Gao, Yin, Zheng and the last author [37] constructed the spectral measure and further proved the time decay and Strichartz estimates of Klein-Gordon equation.…”

Section: Introductionmentioning

confidence: 96%

Generalized Strichartz estimates for wave and Dirac equations in Aharonov–Bohm magnetic fields

Cacciafesta

Yin

Zhang

2022

Dynamics of Partial Differential Equations

View full text Add to dashboard Cite

show abstract

“…Thanks to the above disperive estimate (2.2) and an argument of Keel-Tao [25], one obtains some Strichartz estimates as stated below. 33,22]). Let α ∈ R \ Z, T > 0 and u the solution of (2.1).…”

Section: Useful Tools and Auxiliary Resultsmentioning

confidence: 99%

“…The dispersive and Strichartz estimates are fundamental tools in studying the linear and nonlinear dynamics for dispersive equations. In our setting, we refer to [17,33]. See also [18,Theorem 2.3,p.…”

Section: The Vector Potentialmentioning

confidence: 99%

See 1 more Smart Citation

Well-posedness and scattering for a 2D inhomogeneous NLS with Aharonov-Bohm magnetic potential

Majdoub¹,

Saanouni²

2023

Preprint

View full text Add to dashboard Cite

We consider the magnetic nonlinear inhomogeneous Schrödinger equationwhere α ∈ R \ Z, ̺ > 0, p > 1. We prove a dichotomy of global existence and scattering versus blow-up of energy solutions under the ground state threshold in the inter-critical regime. The scattering is obtained by using the new approach of Dodson-Murphy (A new proof of scattering below the ground state for the 3D radial focusing cubic NLS, Proc. Am. Math. Soc. ( 2017)). This method is based on Tao's scattering criteria and Morawetz estimates. The novelty here is twice: we investigate the case ̺α = 0 and we consider general energy initial data (not necessarily radially symmetric). The particular case α = 0, known as INLS, was widely investigated in the few recent years. Moreover, the particular case ̺ = 0, which gives the homogeneous regime, was considered recently by X. Gao and C. Xu (Scattering theory for NLS with inverse-square potential in 2D, J. Math. Anal. Appl. ( 2020)), where the scattering is proved for spherically symmetric datum. In the radial framework, the above problem translate to the INLS with inverse square potential, which was widely investigated in space dimensions higher than three. The Hardy inequality |x|fails in two space dimensions. Thus, it is not clear how to treat the NLS with inverse square potential in H 1 for two space dimensions. This article seems to be the first one dealing with the NLS with Aharonov-Bohm magnetic potential in the inhomogeneous regime, namely ̺ = 0.

show abstract