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Stability of the Kolmogorov-Zakharov spectrum of weak turbulence

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Weakly turbulent waves can be described by the kinetic wave equation. The first part of the talk will present results on the derivation of this effective equation from a microscopic system described by the nonlinear Schrodinger equation. This kinetic wave equation has isotropic steady states called Kolmogorov-Zakharov spectra, that represent cascades of mass and energy between from small spatial scales toward large ones and conversely. The second part of the talk will discuss the stability of the spectrum associated to the indirect mass cascade. This is based on joint works with I. Ampatzoglou, H. Dietert, and P. Germain.

This talk is part of the Partial Differential Equations seminar series.

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