Gérard, Patrick and Lenzmann, Enno and Pocovnicu, Oana and Raphael, Pierre. (2018) A Two-Soliton with Transient Turbulent Regime for the Cubic Half-Wave Equation on the Real Line. Annals of PDE, 4 (7).
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Abstract
We consider the focusing cubic half-wave equation on the real line
i∂tu+|D|u=|u|2u, |D|uˆ(ξ)=|ξ|u^(ξ), (t,x)∈R+×R.
We construct an asymptotic global-in-time compact two-soliton solution with arbitrarily small L2-norm which exhibits the following two regimes: (i) a transient turbulent regime characterized by a dramatic and explicit growth of its H1-norm on a finite time interval, followed by (ii) a saturation regime in which the H1-norm remains stationary large forever in time.
i∂tu+|D|u=|u|2u, |D|uˆ(ξ)=|ξ|u^(ξ), (t,x)∈R+×R.
We construct an asymptotic global-in-time compact two-soliton solution with arbitrarily small L2-norm which exhibits the following two regimes: (i) a transient turbulent regime characterized by a dramatic and explicit growth of its H1-norm on a finite time interval, followed by (ii) a saturation regime in which the H1-norm remains stationary large forever in time.
Faculties and Departments: | 05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Analysis (Lenzmann) |
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UniBasel Contributors: | Lenzmann, Enno |
Item Type: | Article, refereed |
Article Subtype: | Research Article |
Publisher: | Springer |
ISSN: | 2199-2576 |
Note: | Publication type according to Uni Basel Research Database: Journal article |
Identification Number: | |
Last Modified: | 30 Aug 2018 12:45 |
Deposited On: | 01 Jun 2018 09:25 |
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