Small data scattering of 2d Hartree type Dirac equations

Cho, Yonggeun; Lee, Kiyeon; Ozawa, Tohru

doi:10.1016/j.jmaa.2021.125549

Cited by 8 publications

(11 citation statements)

References 24 publications

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“…As known result for the equation (1.4), Bejenaru and Herr([3]) showed the GWP in H 1 2 (R 2 ). And the known results for the equation (1.5) are in [8,20]. In [20], An author of this paper revealed the LWP in H s (R 2 ) with s > γ−1 2 and 1 ≤ γ < 2.…”

Section: Introductionmentioning

confidence: 79%

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Local well-posedness of Dirac equations with nonlinearity derived from honeycomb structure in 2 dimensions

Lee

2021

Preprint

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Section: Introductionmentioning

confidence: 79%

“…In [20], An author of this paper revealed the LWP in H s (R 2 ) with s > γ−1 2 and 1 ≤ γ < 2. It was studied in [8] that global well-posedness and small data scattering holds in H s (R 2 ) for s > γ − 1 and 1 < γ < 2. As related to (1.5), there is a Dirac equation with Yukawa potential.…”

Section: Introductionmentioning

confidence: 99%

Local well-posedness of Dirac equations with nonlinearity derived from honeycomb structure in 2 dimensions

Lee

2021

Preprint

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“…Recently small data scattering results for the equation (1.5) have been well-known. For instance see [6,7,8,16,17,18] and references therein. We also refer to [10], which concerns global solutions for large H s -data in R 1+2 .…”

Section: Introductionmentioning

confidence: 99%

Conditional large-data global well-posedness of Dirac equation with Hartree-type nonlinearity

Cho¹,

Hong²,

Lee³

2022

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We study the Cauchy problems for the Hartree-type nonlinear Dirac equations with Yukawa-type potential in two and three spatial dimensions. This paper improves our previous results [7,6]; we establish global well-posedness and scattering for large data with a certain condition. Firstly we investigate the long-time behavior of solutions to the Dirac equation satisfies good control provided that a particular dispersive norm of solutions is bounded. The key of our proof relies on modifying multilinear estimates obtained in our previous papers.Secondly, we obtain large data scattering by exploiting the Majorana condition.

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“…x for (1.1) with the Coulomb potential V 0 (x) = 1 4π|x| . In view of [5,19,7], there are trivial scattering conditions of (1.1). However, as observed in [7] for 2D problem, such scattering cannot occur for a certain class of solutions.…”

Section: Introductionmentioning

confidence: 99%

“…In view of [5,19,7], there are trivial scattering conditions of (1.1). However, as observed in [7] for 2D problem, such scattering cannot occur for a certain class of solutions. To be precise, let us define I as follows:…”

Section: Introductionmentioning

confidence: 99%

Scattering and non-scattering of the Hartree-type nonlinear Dirac system at critical regularity

Cho,

Hong,

Lee

2021

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We consider Cauchy problem of the Hartree-type nonlinear Dirac equation with potentials given by V b (x) = 1 4π e −b|x| |x| (b ≥ 0). In previous works, a standard argument is to utilise null form estimates in order to prove global well-posedness for H s -data, s > 0. However, the null structure inside the equations is not enough to attain the critical regularity. We impose an extra regularity assumption with respect to the angular variable. Firstly, we prove global wellposedness and scattering of Dirac equations with Hartree-type nonlinearity for b > 0 for small L 2x -data with additional angular regularity. We also show that only small amount of angular regularity is required to obtain global existence of solutions. Secondly, we obtain non-scattering result for a certain class of solutions with the Coulomb potential b = 0.

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Small data scattering of 2d Hartree type Dirac equations

Cited by 8 publications

References 24 publications

Local well-posedness of Dirac equations with nonlinearity derived from honeycomb structure in 2 dimensions

Local well-posedness of Dirac equations with nonlinearity derived from honeycomb structure in 2 dimensions

Conditional large-data global well-posedness of Dirac equation with Hartree-type nonlinearity

Scattering and non-scattering of the Hartree-type nonlinear Dirac system at critical regularity

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