Geodesic
Singularities in the weak turbulence regime for the quintic Schrödinger equation
Documenta mathematica, Tome 27 (2022), pp. 2491-2561

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In this paper, we discuss the problem of derivation of kinetic equations from the theory of weak turbulence for the quintic Schrödinger equation. We study the quintic Schrödinger equation on LT, with L≫1 and with a non-linearity of size ε≪1. We consider the correlations f(T) of the Fourier coefficients of the solution at times t=Tε−2 when ε→0 and L→∞. Our results can be summed up in the following way: there exists a regime for ε and L such that for T dyadic, f(T) has the form expected from the Physics literature for kinetic regimes, but such that f has an infinite number of discontinuity points. This discontinuity appears in the context of finite-box effects.
DOI : 10.4171/dm/x35
Classification : 35Q35, 35Q41
Mots-clés : Schrödinger equations, discrete weak turbulence, Wick renormalisation 
Anne-Sophie de Suzzoni. Singularities in the weak turbulence regime for the quintic Schrödinger equation. Documenta mathematica, Tome 27 (2022), pp. 2491-2561. doi: 10.4171/dm/x35
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     author = {Anne-Sophie de Suzzoni},
     title = {Singularities in the weak turbulence regime for the quintic {Schr\"odinger} equation},
     journal = {Documenta mathematica},
     pages = {2491--2561},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/x35},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/x35/}
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