We prove local existence and uniqueness results for the (space-homogeneous) 4-wave kinetic equation in wave turbulence theory. We consider collision operators defined by radial, but general dispersion relations satisfying suitable bounds, and we prove two local well-posedness theorems in nearly critical weighted spaces.
All Science Journal Classification (ASJC) codes
- Nonlinear Schrödinger
- Quantum Boltzmann
- Wave (weak) turbulence
- Wave kinetic equations