On the radius of spatial analyticity for cubic nonlinear Schrödinger equations

Tesfahun, Achenef

doi:10.1016/j.jde.2017.08.009

Cited by 38 publications

(23 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…and again obtain the desired bound (27). It remains to consider the subcase L max = L 0 of case (i).…”

Section: 1mentioning

confidence: 97%

“…The investigation of spatially uniform lower bounds on the radius of analyticity for nonlinear evolutionary PDE was initiated by Kato and Masuda [19], and by now there is an extensive catalog of results along these lines for various nonlinear PDE, including the Kadomtsev-Petviashvili equation [6], the (generalized) Korteweg-de Vries equation [18,4,24], the Euler equations [20], the cubic Szegő equation [15] and the nonlinear Schrödinger equation [17,5,27].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the radius of spatial analyticity for solutions of the Dirac–Klein–Gordon equations in two space dimensions

Selberg

2019

Ann. Inst. H. Poincaré C Anal. Non Linéaire

View full text Add to dashboard Cite

We consider the initial value problem for the Dirac-Klein-Gordon equations in two space dimensions. Global regularity for C ∞ data was proved by Grünrock and Pecher. Here we consider analytic data, proving that if the initial radius of analyticity is σ 0 > 0, then for later times t > 0 the radius of analyticity obeys a lower bound σ(t) ≥ σ 0 exp(−At). This provides information about the possible dynamics of the complex singularities of the holomorphic extension of the solution at time t. The proof relies on an analytic version of Bourgain's Fourier restriction norm method, multilinear space-time estimates of null form type and an approximate conservation of charge.

show abstract

“…and again obtain the desired bound (27). It remains to consider the subcase L max = L 0 of case (i).…”

Section: 1mentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

On the radius of spatial analyticity for solutions of the Dirac–Klein–Gordon equations in two space dimensions

Selberg

2019

Ann. Inst. H. Poincaré C Anal. Non Linéaire

View full text Add to dashboard Cite

show abstract

“…Following the argument in [19], we first consider the case s = 1. By the embedding (1.3), the general case s ∈ R will reduce to s = 1 as shown in the end of this section.…”

Section: Proof Of Theorem 11mentioning

confidence: 99%

On the radius of spatial analyticity for defocusing nonlinear Schrödinger equations

Ahn¹,

Kim²,

Seo³

2020

Discrete &Amp; Continuous Dynamical Systems - A

View full text Add to dashboard Cite

In this paper we study spatial analyticity of solutions to the defocusing nonlinear Schrödinger equations iut + ∆u = |u| p−1 u, given initial data which is analytic with fixed radius. It is shown that the uniform radius of spatial analyticity of solutions at later time t cannot decay faster than 1/|t| as |t| → ∞. This extends the previous work of Tesfahun [19] for the cubic case p = 3 to the cases where p is any odd integer greater than 3.2010 Mathematics Subject Classification. Primary: 32D15; Secondary: 35Q55.

show abstract

“…The main ingredients in our proof are almost conservation law for the solution to the KdV equation in spaces of analytic functions and spacetime dyadic bilinear estimates associated with the KdV equation. For similar studies for the Dirac-Klein-Gordon system, generalized KdV and cubic NLS see [32,16,31,34]. For studies on related issues for nonlinear partial differential equations see for instance [5,6,7,9,14,17,8,15,18,28,19,29,26].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic lower bound for the radius of spatial analyticity to solutions of KdV equation

Tesfahun

2019

Commun. Contemp. Math.

Self Cite

View full text Add to dashboard Cite

It is shown that the uniform radius of spatial analyticity σ(t ) of solutions at time t to the KdV equation cannot decay faster than |t | −4/3 as |t | → ∞ given initial data that is analytic with fixed radius σ 0 . This improves a recent result of Selberg and Da Silva, where they proved a decay rate of |t | −(4/3+ε) for arbitrarily small positive ε. The main ingredients in the proof are almost conservation law for the solution to the KdV equation in space of analytic functions and space-time dyadic bilinear L 2 estimates associated with the KdV equation. 1991 Mathematics Subject Classification. 35Q53; 35L30. Key words and phrases. KdV equation; Radius of spatial analticity; Asymptotic lower bound .1 4.3. Local well-posedness in Gevery class. Define the map Φ(u)(t ) = χ(t /4)W (t ) f + B(u, u)(t ). Let s ∈ [−3/4, 0] and J = [−1, 1]. By Lemma 7(ii), (iii) and Corollary 2 we have Φ(u) X σ,s J

show abstract

On the radius of spatial analyticity for cubic nonlinear Schrödinger equations

Cited by 38 publications

References 15 publications

On the radius of spatial analyticity for solutions of the Dirac–Klein–Gordon equations in two space dimensions

On the radius of spatial analyticity for solutions of the Dirac–Klein–Gordon equations in two space dimensions

On the radius of spatial analyticity for defocusing nonlinear Schrödinger equations

Asymptotic lower bound for the radius of spatial analyticity to solutions of KdV equation

Contact Info

Product

Resources

About