Local error of a splitting scheme for a nonlinear Schrödinger-type equation with random dispersion

Marty, Renaud

doi:10.4310/cms.2021.v19.n4.a8

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Cited by 7 publications

(1 citation statement)

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“…x ∩ H 1 x exist globally and satisfy the average decay estimate E u(t) L ∞ x (1 + t) −1/4 . There have also been several works considering numerical schemes for (1) [6,18,19,30,33].…”

Section: Introductionmentioning

confidence: 99%

On the wellposedness for periodic nonlinear Schrödinger equations with white noise dispersion

Stewart¹

2022

Preprint

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We study the wellposedness of the periodic nonlinear Schrödinger equation with white noise dispersion and a power nonlinearity given byWe develop Strichartz estimates for this equation, which we then use to prove almost sure global wellposedness of this equation with L 2 initial data for nonlinearities with exponent 1 < p ≤ 3. By generalizing the Fourier restriction spaces X s,b to the stochastic setting, we also prove that our solutions agree with the ones constructed by Chouk and Gubinelli (Commun. Part. Diff. Eq. 40(11):2047-2081 using rough path techniques. We also consider the quintic equation (p = 5), and show that it is analytically illposed in L 1 ω CtL 2 x .

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“…x ∩ H 1 x exist globally and satisfy the average decay estimate E u(t) L ∞ x (1 + t) −1/4 . There have also been several works considering numerical schemes for (1) [6,18,19,30,33].…”

Section: Introductionmentioning

confidence: 99%

On the wellposedness for periodic nonlinear Schrödinger equations with white noise dispersion

Stewart¹

2022

Preprint

View full text Add to dashboard Cite

show abstract

On the wellposedness of periodic nonlinear Schrödinger equations with white noise dispersion

Stewart¹

2023

Stoch PDE: Anal Comp

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Analysis of a splitting scheme for a class of nonlinear stochastic Schrödinger equations

Bréhier

Cohen

2023

Applied Numerical Mathematics

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Local error of a splitting scheme for a nonlinear Schrödinger-type equation with random dispersion

Abstract: We study a Lie splitting scheme for a nonlinear Schrödinger-type equation with random dispersion. The main result is an approximation of the local error. Then we can deduce sharp order estimates, for instance in the case of a white noise dispersion.

Cited by 7 publications

References 10 publications

On the wellposedness for periodic nonlinear Schrödinger equations with white noise dispersion

On the wellposedness for periodic nonlinear Schrödinger equations with white noise dispersion

On the wellposedness of periodic nonlinear Schrödinger equations with white noise dispersion

Analysis of a splitting scheme for a class of nonlinear stochastic Schrödinger equations

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