On the ill-posedness of kinetic wave equations

2024/11/19 by Ioakeim Ampatzoglou, Ampatzoglou, Ioakeim, Tristan Léger +1 · 1 citation
Physics and Astronomy · Computer Science · Mathematics · #Quantum chaos and dynamical systems #Nonlinear Dynamics and Pattern Formation #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2411.12868

Abstract

In this article we identify a sharp ill-posedness/well-posedness threshold for kinetic wave equations (KWE) derived from quasilinear Schrödinger models. We show well-posedness using a collisional averaging estimate proved in our earlier work \citeAmLe. Ill-posedness manifests as instantaneous loss of smoothness for well-chosen initial data. We also prove that both the gain-only and full equation share the same well-posedness threhold, thus legitimizing a gain-only approach to solving 4-wave kinetic equations.

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