Strichartz estimates in Wiener amalgam spaces and applications to nonlinear wave equations

In this paper, we obtain some new Strichartz estimates for the Dirac flow in the context of Wiener amalgam spaces which control the local regularity of a function and its decay at infinity separately unlike spaces. While it is well understood recently for some flows such as the Schrödinger and wave flows that work in the non‐relativistic regime, nothing is known about the Dirac flow which governs a physical system in the case of relativistic fields.

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“…These aspects were originally pointed out in the several works by Cordero and Nicola [2–4] in the context of the Schrödinger flow

\text{e}^{\text{i}t\Delta }

, and the works were generalized in [11] to initial data with regularity. See also [12] for the wave flow

\text{e}^{\text{i}t\sqrt {-\Delta }}

.…”

Section: Introductionmentioning

confidence: 99%

“…This is because the spinorial structure of Dirac propagator is not harmful any more for obtaining the decay estimates by virtue of the projections. It is worth noticing that some relevant decay estimates were already known in [12] for the wave propagator. This would yield the results with some modification for the massless case.…”

Section: Introductionmentioning

confidence: 99%

Strichartz estimates for the Dirac flow in Wiener amalgam spaces

Kim

Lee

Seo

2023

Mathematische Nachrichten

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show abstract

“…These aspects were originally pointed out in the several works by Cordero and Nicola ([2,3,4]) in the context of the Schrödinger flow e it∆ , and the works were generalized in [11] to initial data with regularity. See also [12] for the wave flow e it √ −∆ . As such, the results known so far are for the flows that work in the non-relativistic regime.…”

Section: Introductionmentioning

confidence: 99%

Strichartz estimates for the Dirac flow in Wiener amalgam spaces

Kim¹,

Lee²,

Seo³

2022

Preprint

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In this paper we obtain some new Strichartz estimates for the Dirac flow in the context of Wiener amalgam spaces which control the local regularity of a function and its decay at infinity separately unlike L p spaces. While it is well understood recently for some flows such as the Schrödinger and wave flows that work in the non-relativistic regime, nothing is known about the Dirac flow which governs a physical system in the case of relativistic fields.

show abstract

Strichartz estimates in Wiener amalgam spaces and applications to nonlinear wave equations

Cited by 2 publications

References 17 publications

Strichartz estimates for the Dirac flow in Wiener amalgam spaces

Strichartz estimates for the Dirac flow in Wiener amalgam spaces

Strichartz estimates for the Dirac flow in Wiener amalgam spaces

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